Martin J. Silverthorne
Super Slots!
SILVERTHORNE
PUBLICATIONS
Super Slots
COPYRIGHT © 2008 by Silverthorne Publications Inc.
All rights reserved. Except for brief passages used in legitimate
reviews, no parts of this book may be reproduced or utilized in any form
or by any means, electronic or mechanical, without the written
permission of the publisher.
Address all inquiries to the publisher:
Silverthorne Publications, Inc.
848 N. Rainbow Blvd., Suite 601
Las Vegas, Nevada 89107
United States of America
www.silverthornepublications.com
The material contained in this book is intended to inform and
educate the reader and in no way represents an inducement to
gamble legally or illegally.
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TABLE OF CONTENTS
Introduction
3
Types of Slots
8
The Mathematics of Slots
22
Finding the Best Machines
35
The Ladder Approach
51
Cycle Testing Slots
69
Winning With Cycle Betting
87
Money Management
97
Slots and the IRS
114
Winning With the Super System
117
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INTRODUCTION
There is no doubt that the future of casino gaming lies with
the slot machines. In most casinos the "one-armed bandits" are
steadfastly encroaching on the territories formerly reserved for
table games, and in some cases even by gift shops or restaurants.
Walking through a casino and observing people inserting
coins into slots and pulling handles as fast as they can while
accompanied by a never ending background noise of bells,
whistles, musical tunes and the screams of delight of winners
possibly surpasses the excitement of being a spectator at a Roman
circus.
Some casino executives have even toyed with the idea of
putting slot machines in the patrons rooms, so that a true addict
can play without even bothering to get dressed.
The casinos love the slot machines because they produce
revenue for the casinos at a lower cost than the table games.
Instead of having to hire and train whole crews of dealers, pit
bosses and floormen, a few attendants can service a slew of slots.
Players love slots because they don't have to know anything to
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participate. Slots are easy to understand, easy to play, and in the
case of some progressive machines, can net a player a win worth
millions of dollars.
No wonder slots are expanding faster than any other casino
game. There is no question in my mind that slots are addictive
too! As I write this, there is considerable discussion in the news
media concerning the addictiveness of nicotine. Without question,
growing numbers of persons are becoming just as addicted to slots
as the nicotine addicts are to their tobacco products.
Unfortunately, just like everything else in the world, slots
are not as simple as they used to be. All of the new versions of
slots are computer controlled, with mind staggering numbers of
possible winning and losing combinations "built-in" to the slot's
programming.
In order to win at slots today, you need to recognize that
the game is not the same as it was twenty years ago. In that
bygone period, most slots were far simpler than they are today.
Many persons wax nostalgic for those less complicated days on
many more topics than only slot machines.
Our purpose is to look at slots as they are played now, and
as they will be played into the next century. A fundamental
question is "can the computer controlled modern slots be beaten
on a regular basis?" If your purpose in reading this book is to
learn a single gimmick that can be used to beat all slots, in all
locations, at all times, you will be disappointed. There is no such
animal.
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However, if you are willing to invest a little time, to learn
about the different types of slot machines, to find a slot with a
good opportunity of winning, and then apply some specific
techniques to the game, you have come to the right place.
My objective in writing Super Slots is to discuss in some
detail some winning techniques which can be applied to many
different versions of slot machines. I feel that the purpose of
playing slots is to win and I hope you share this perspective. We
may have some fun along the way, as slots are supposed to be fun,
but we will not lose sight of our principle objective of winning.
In doing background research for this book, I assembled a
large library of slots books, reports, systems, strategies and just
plain superstitions. Because of my own background as a
successful businessman with a grasp of mathematics, I brought my
own prejudices to my study of this subject. I believe that any
winning technique must be based on observed empirical evidence,
must be explainable in rational terms and most importantly, must
be repeatable. As an example, assume that I just completed a very
successful trip to Las Vegas and I won a $1,000,000 slot jackpot.
Would it do you any good to know what time of day I played, or
what I had for lunch or what I was wearing when I won the
jackpot? Could any of these factors possibly aid you in repeating
my feat of winning a million dollars?
Unfortunately, much of what has been written about slots
falls into this category of "look what I did," or "see what others
have done." This information is generally of very little value
except for entertainment purposes.
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While I hope that you will at least find this book interesting
and hopefully somewhat entertaining, this is not my purpose in
writing it. My purpose is to share with you empirical, and
therefore verifiable, evidence that using a technique which will be
described in some detail, will allow you to win regularly on slot
machines.
If you judge by what others have written on the subject,
there is no method that you can use to regularly win on the slots.
My review of slots literature was primarily anecdotal, and, as it
turned out, merely provided a background of mostly what not to
do.
The information developed for this book has been the
product of original research. I used my own wits and a degree of
common sense to approach this subject and I believe that you will
find that the fruits of this labor are of some value to you.
This book is organized in such a way that we will progress
one step at a time in reaching our goal. We will explore the world
of slot machines, as there are almost as many types of slots as
there are people, and like people, not all slots are created equal.
We will look into the mathematics of slot machines. How
are the slots programmed to pay off, and how can we exploit this
knowledge to our benefit?
We will learn how to zero in on the best slots in the best
locations. From there we will begin building our winning
approach to playing slots. When we have completed this process,
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we will be well equipped to tackle the one-armed bandits. We will
look into the law as it pertains to slots and finally we will
reexamine and refine our winning slots strategy.
Some parts of this journey may require a second or even a
third reading to grasp the concepts. Let me encourage you to do
so, as the results should more than justify the effort.
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TYPES OF SLOTS
The origin of the slot machine is traced back to 1887 and its
inventor, Charles Fey. Fey's slots contained three reels featuring
Bells, Hearts, Diamonds, Spades, Horseshoes and Stars. These
slots accepted one nickel at a time and featured a top payout of ten
nickels.
Fey did not sell his machines but placed them in saloons on
a 50-50 profit split arrangement with the proprietors. In 1929,
forty-two years later, Fey built the first slot machine to take a
silver dollar. That machine had three reels with fruit and bar
symbols and had a top jackpot of $100.
These early machines proliferated, with additional
manufacturers, such as Herbert Mills and O. D. Jennings joining
the fray. Many different versions of these slots were produced
over the years, but all shared similar mechanical parts and
produced the familiar slot machine sounds of clicking and
clanging as the parts moved around.
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By the late 1950s a new breed of slot began appearing.
These machines were electrically powered and featured such
innovations as multiple coin play, progressive jackpots and many
more anti-cheating safeguards than the old mechanical machines.
By the 1970s manufacturers began using solid state
circuitry to develop the first totally electronic slots machines.
These machines were short lived as solid state technology was
replaced by microprocessors.
Microprocessors are commonly called "chips" and are
really miniature computers working with other electronic
components using integrated circuits to control the machines.
Here the microprocessor controls all aspects of the slot including
the reels.
Programmed into each slot are formulas which are
translated into certain combinations and arrangements of the
symbols which appear on the reels. As part of this process,
random numbers are generated by the microprocessor and these
numbers are used to determine the symbols appearing on the reels
and consequently, the payoffs.
Because of the reliability of micro-technology, these slots
are more predictable than the earlier mechanical or electrically
powered slots. If a machine has been programmed to pay off
94.3% of all coins played into it, then over a reasonable amount of
time, this machine will perform very close to this specification.
The casinos like the microprocessor controlled machines because
of their reliability and predictability. Many players bemoan the
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decline of the mechanical slots for the very reason that these
machines were more likely to malfunction and perform such feats
of generosity as overpaying the players.
The single coin slots are a thing of the past, having passed
away with the demise of the mechanical slot machines. You may
still find some of the old mechanical slots at roadside locations.
They are usually nickel machines with jackpots of just a few
dollars.
Modern slot machines accept more than one coin and will
multiply the size of the payoff by the number of coins played.
Because of this feature these machines are known as multipliers.
Most of these machines accept three to five coins maximum per
pull although some types will accept 8, 9 or even 10 coins.
Most of the multipliers have a single payline across the reel
display area. All payoffs are based on the combinations of
symbols showing after the reels have come to rest. The multiplier
aspect increases the payoff for each winning combination of
symbols. In some cases, a bonus may be paid for playing the
maximum number of coins if the machine hits the highest jackpot.
For example, on a three reel machine where 7 7 7 is the
highest payoff, the slot may pay 100 coins for one coin played,
200 coins if two coins are played and 600 coins if three coins are
played. The payout for a jackpot with three coins played has a
bonus of 300 coins offered. Many of the progressive slots, which
offer increasing jackpots as the machine receives more play, are
structured along the lines of the bonus machine, with the jackpot
paid only if the maximum number of coins are played.
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The casino's rationale in offering the bonus or jackpot for
playing three coins per pull is to entice more players into always
playing the maximum number of coins.
Many multipliers do not offer bonuses for playing the
maximum number of coins. These machines increase the payoffs
proportionately to the number of coins played, with no bonuses for
playing with the maximum number of coins.
Multipliers that do not offer the bonus feature can be
played as single coin machines as well as multi-coin machines
without sacrificing any advantage in the payoffs.
Table 1 shows the pay schedule for a typical 3 Reel 3 Coin
Multiplier. We will refer to this type of machine as a Standard 3
Coin Multiplier.
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Table 1. Standard 3 Coin Multiplier
Symbols
1
Coin
2
Coins
3
Coins
Cr Cr Cr
50
100
150
B B Bar
15
30
45
DBC DBC Bar
15
30
45
Bar Bar Bar
10
20
30
Ch Ch Ch
10
20
30
B B B
5
10
15
DBC DBC DBC
5
10
15
Any 1 C
2
4
6
Cr = Crown
B = Bell
Bar = Bar
Ch = Cherry
DBC = Double Bar Cherry
On a Standard Multiplier, as shown in Table 1, payoffs
increase exactly proportionately to the number of coins inserted.
We can play one, two or three coins on such a machine with no
penalty for not inserting the maximum number of coins.
Table 2 shows a Standard 5 Coin Multiplier for a slot
with three reels. Like the 3 coin version, there is no penalty for
not playing the maximum number of coins.
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Table 2. Standard 5 Coin Multiplier
Symbols
1
Coin
2
Coins
3
Coins
4
Coins
5
Coins
TC TC TC
100
200
300
400
500
DC DC DC
20
40
60
80
100
C C C
10
20
30
40
50
Any 3 Cherries
2
4
6
8
10
TC = Triple Cherry
DC = Double Cherry
C = Cherry
Progressive Slot machines pay much larger jackpots only
when the maximum number of coins are played. Table 3 shows
the payoffs for a three reel slot with a progressive jackpot of over
25,000 coins. This jackpot is paid when 7 7 7 lines up and the full
jackpot amount will only be paid when three coins have been
played.
The Option play machine, also called the Buy-a-Pay slot
machine, can be very confusing. With these machines, each coin
inserted brings into play additional symbols offering payoffs.
There is nothing on these machines to specifically identify them as
option machines. You must read the payout schedule on the front
of the machine carefully to spot one of these critters.
Table 4 shows the payoff schedule for an Option 3 Coin
Multiplier. Playing one or two coins brings the payoff schedule,
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shown on the left side of the table, into play. Only when three
coins are played do the symbols on the right side of the table come
into play. If you had played two coins and the symbols C C C
appeared, your payoff would be zero, as this combination of
symbols pays off only when three coins are inserted.
Table 3. Progressive 3 Coin Multiplier
Symbols
1
Coin
2
Coins
3
Coins
777
100
200
Jackpot
B B Bar
15
30
45
O O Bar
15
30
45
CCC
10
20
30
Bar Bar Bar
5
10
15
OOO
5
10
15
BBB
5
10
15
Any 1 Cherry
2
4
6
7 = Seven
B = Bell
Bar = Bar
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O = Orange
C = Cherry
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Table 4. Option 3 Coin Multiplier
Symbols
1
Coin
2
Coins
3
Coins
Symbols
3
Coins
$$$
50
100
200
CCC
300
BBB
10
20
30
BBB
60
--B
2
4
6
SSS
60
Any 2H
2
4
6
$--
15
$ = Dollar Sign
B = Money Bag
H = Heart
S = Spade
D = Diamond
C = Club
The Option type of slots offers limited possibilities of
playing from one to the maximum number of coins as playing less
than the maximum number of coins reduces the number of
combinations of symbols offering payoffs.
Another version of slot machine, which requires maximum
coin play in order to bring all of the payoff combinations into play,
is the Multiple Pay Line machine. Instead of offering only one
pay line, there may be two, three or even five pay lines. As each
additional coin is inserted, another pay line comes into play. Like
many of the multipliers, the jackpots or jackpot bonuses are
available only on the last payline, so that you have to play the
maximum number of coins to win the jackpot. Table 5 shows the
payoffs for a 3 reel, 2 coin multiple pay line slot. While the payoff
symbols are the same whether one or two coins are inserted, the
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second pay line only comes into play with the insertion of the
second coin.
Table 5. Multiple Pay Line 2 Coin Multiplier
Symbols
1 or 2 Coins
Cr Cr Cr
100
O O O
20
A A A
10
B B -
5
- B B
5
S S -
5
- S S
5
Any 1 Cr
1
First coin activates first pay line, second coin, second pay line.
Cr = Crown
B = Banana
O = Orange
S = Strawberry
A = Apple
Each of the examples of payoff tables shown here are
merely representative examples. There are hundreds of variations
of slot payoffs and in order to determine the type of slot you are
about to play, you must read the payoff schedule shown on the
front of the machine.
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On the multiplier slots, the insertion of each coin will cause
a different section of the payoff schedule to light up, showing the
applicable payoffs for the number of coins played. Always make
sure that each coin inserted causes this to happen. If you insert a
coin which doesn't register, and then pull the handle without
verifying its registration, you will not be paid the full amount of a
payoff. If a machine does not register a coin played, you should
immediately notify a slot attendant.
The progressive slot machines have brought a new glamour
to slot machines. The million dollar plus jackpots you hear about
people winning are won on progressive slots.
With a progressive slot machine, the jackpot is increased
each time the machine is played. Progressive slot machines are
multipliers which keep adding to the jackpot until it is hit.
The progressive machines can be found in two different
types of setups. The older and more common types of
progressives are individual free-standing machines which will be
found either by themselves or in a designated area with other
jackpot machines. These machines operate independently of each
other so that each machine's jackpot is unaffected by any other slot
machine.
In response to the state lotteries, slot machine
manufacturers have developed machines which are linked together
and share the same jackpot. The machines, called LinkProgressives are even linked between different casinos. Each
machine in the system contributes to the jackpot which continues
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to grow with each play on a machine in the system. Many of these
machines receive enough play to cause the jackpot to grow by a
hundred thousand dollars or more per week.
The MEGABUCKS system, introduced by IGT
Corporation, is a prominent example of a link-progressive system
with different casinos participating. MEGABUCKS jackpots
often total in the millions of dollars.
There are many other variations of slot machines. Some
slot machines pay only jackpots. With these Jackpot-Only
machines, all of the symbols offering smaller payoffs have been
removed from the reels. You can spot these machines fairly easily
as there are many blank spots, sometimes called "ghosts" on the
reels. With these machines, the payoffs are very infrequent.
Other varieties of slots are the giant slot machines or "Big
Berthas." These monsters have up to eight reels, are slow to play,
and have terrible payoffs. The Four Queens in downtown Las
Vegas boasts the world's largest slot called "The Queen's Throne."
The machine is designed for one to six players, who sit in
"thrones" around this behemoth. The odds of hitting the big
jackpot on this Bertha could be as high as 55 billion to one!
Video slots have been coming on very strongly the past few
years, with video poker leading the pack. Instead of levers, the
machines are activated by buttons and offer the players the chance
to influence the outcome of each play through the exercise of skill,
rather than pure chance. In addition to video poker machines,
there are video blackjack, video keno, video horse racing and
video craps.
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The most popular of the video slots is unquestionably video
poker, with the five card draw version reigning supreme. Here the
degree of the player's skill in determining which of five cards
drawn on an initial hand to hold and which to discard can have a
major impact on the his ability to win. Certain versions of the
game offer the opportunity of playing at an advantage to the
casino, if the player's skill is up to it. While video poker is beyond
the scope of this book, two excellent books have been written on
the game. Winning With Expert Video Poker covers all the major
versions of video poker and shows specific strategies the player
can use to beat the game. Beat Joker Poker!, which I wrote,
focuses on the Joker Wild version of video poker and has
complete strategies for playing with player advantage. Both books
are available through Silverthorne Publications, the publisher of
this book.
A final category of slots are the specialty machines, such as
the pusher games. Pusher machines are based on an old arcade
game and have two or three shelves of coins which are pushed
around by paddles. When the machine is played by inserting coins
into one to four slots, an impeller shoots the coin up onto the
shelves for an instant win in one of the five holes on the wall
above the shelves. If your coin misses the hole, it may knock
other coins off the shelves and into the payout chute below. This
game and other carnival like games such as horse racing, should
be played for amusement only as the winning prospects are very
poor.
With the large variety of slot machines, it is no easy task to
pick the right machine. One of the most important things to do in
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picking a machine is to carefully read the instructions and payoffs
before beginning to play it.
The strategies developed in this book will focus on only
certain of the multipliers. We have presented several tables in this
chapter so that you can become familiar with the differences
between multipliers. You should be able to easily distinguish
between a Standard 3 or 5 Coin Multiplier and a Progressive
Multiplier or an Option or Multiple Pay Line Multiplier.
Other aspects of picking the best machine to play are the
house advantage on the machine, the exact configuration of the
machine's payoffs, your bankroll, the time you have available to
play and your ability to follow and adhere to a defined strategy.
We shall explore each of these aspects as we continue our journey.
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THE MATHEMATICS OF SLOTS
All gaming machines are designed to pay the player back a
percentage of what is played. The amounts vary from machine to
machine and from casino to casino. All machines have one thing
in common: The longer the machine is played, the closer the
actual payouts will be to the theoretical results.
Slot machines use a random selection process to achieve a
set of theoretical odds. Random selection means that each time
the lever is pulled and the reels are set in motion a combination of
symbols are randomly selected. The "random" aspect ensures that
each pull of the handle is independent from every other pull, so
that the results of the previous pull, and the one before that, have
no effect on the current one.
The theoretical odds are built into the design and program
of the machine, and it is possible to calculate the exact payout
percentage for any machine over the long-term.
Except for the video slots, slot machines have wheels called
reels with symbols printed on each wheel. Each reel symbol
represents a stop which may come to rest on the payline, and may
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or may not be part of a combination of symbols resulting in a
payoff.
The likelihood of winning any payoff on any slot machine
is related to the number of reels and the number of symbols on
each reel.
The most common type of mechanical slot machine has
three reels with twenty symbols on each reel. To calculate the
total number of combinations of symbols on this machine, we
multiple the number of stops (symbols) on each reel by the
number of stops on each of the remaining reels. For a three reel
machine with twenty stops per reel, we have 20 x 20 x 20 = 8,000
combinations of slot symbols.
If a jackpot offered on this machine pays on 7 7 7 and only
one 7 symbol is on each reel, then the probability of hitting this
jackpot is 1/20 x 1/20 x 1/20 or one in 8,000. If two 7 symbols are
on one reel, then our calculation is 2/20 x 1/20 x 1/20 for a
probability of 1/4,000 of hitting the jackpot.
Likewise, we can calculate the probability of any
combination of symbols hitting if we know the number of times
each symbol appears on each reel.
When mechanical slots dominated, it was not too difficult
to count the symbols on each reel and determine exactly the payoff
of a given machine. With microprocessor controlled slots this task
has become almost impossible, as the number of stops per reel can
be as many as 256. To determine the payoffs of such a machine
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would require significant reverse engineering and is beyond the
scope of almost every player.
The number of reels has a greater effect on the probabilities
than the number of symbols per reel. If we compare a machine
with 32 stops per reel and 3 reels, with a 22 stop per reel machine
and 4 reels, you will see the tremendous difference another reel
makes:
32 Stop, 3 Reel: 32 x 32 x 32 = 32,768 combinations
22 stop, 4 Reel: 22 x 22 x 22 x 22 = 234,256 combinations
If we consider a 5 reel machine with 32 stops per reel, we
find over 33 million combinations!
Every slot machine has a predetermined payout percentage.
When you hear things like "our slots pay back 98.3%" this means
that over the long-term for every dollar inserted in the machine, it
will return 98.3 cents. Conversely, we could state that as for every
dollar played, the casino will retain 1.7 cents. These percentages
only hold true over very long-term play consisting of hundreds of
thousands or even millions of plays.
Many people misinterpret these percentages and think that
if they play with $100.00 on a 98.3% payback machine that they
can only lose $1.70. There are a couple of things wrong with this
line of thinking. First, theoretical percentages will be attained
only over long periods of play. Over a few dozen, or even a few
hundred rolls, the payback percentage will vary greatly. Secondly,
if a person brings $100.00 for slot play, he or she usually will not
limit his or her play to inserting this amount of money into the
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machine only one time. Most people will buy twenty dollars
worth of tokens and continue to play with this money until it is
gone. After inserting the first round of coins in the machine, they
will continue playing with any coins left in the tray, and they will
continue this pattern until no coins are left. And then they wonder
how it was possible for a 98.3% slot to take all of their money.
The answer is that the casino continues to extract its
percentage on every coin inserted into the machine. The player
will not limit his play to twenty dollars or one hundred dollars but
will continue to redeposit coins. The machine will, at least over
the long-term, continue to grind away at all money played.
Table 6 shows the devastating effect the house edge can
have on the player's bankroll. This table compares slot hold
percentages of from two percent to fifteen percent for ten rounds
of play, starting with $100.
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Table 6. Amount Retained Per Round of Play
Slot Hold %
2%
5%
10%
15%
Start Round
$100
$100
$100
$100
1
98
95
90
85
2
96
90
81
72
3
94
86
73
61
4
92
81
66
52
5
90
77
59
44
6
88
73
53
38
7
86
69
48
32
8
85
66
43
27
9
83
63
39
23
10
81
60
35
20
With a 15% casino hold, there is only $85 left after one
round of play, and after ten rounds the $100 has been reduced to
only $20. If we continue to play the 15% hold game, after twenty
rounds we will be down to about $4. We can see the power of a
hold rate of 15%.
If we contrast this with the 2% hold rate, we see that after
ten games we still retain $81. Even though we have gradually lost
some money on this machine, we can see that hitting a single
higher payoff would put us ahead and that we have gained much
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more playing time to do so. If you never cared what the casino
hold was before, this should open your eyes. It is imperative that
you always seek and play machines with lower hold percentages.
Unfortunately, casinos do not label their machines with the
hold or payback percentages. However, the player's win rates are
available for different locations. Table 7, which shows the win
rates for different United States casino locations, was derived from
information published by the Casino and Gaming Control Boards
and Commissions of Nevada, New Jersey, Illinois, Iowa,
Connecticut and Colorado.
If we were seeking to play the highest payback slots, we
might begin our search with this information. The highest average
payback in the U.S. is in Downtown Las Vegas, with an average
payback of 95.4%. The average for all Nevada casinos is 95.06%.
The next best place to play is in Colorado, with an average rate of
93.06%.
Moving east, we find that the Illinois river boats offer the
third best choice at 92.3%, followed by Foxwoods in Connecticut
with 91.7%, the Iowa's river boats at 91.63%, and in last place the
Atlantic City casinos with an average payback of 91.23%.
We also notice that the win rates increase with the size of
coin accepted, with the nickel slots paying out the lowest
percentages and the five dollar slots the highest. In Nevada, the
win rates average about 95% for all but the lowly nickel slots. So,
on the average, it is safe to say that if we limit our play to Nevada
casinos and avoid the nickel slots, we can expect to receive about
a 95% payback.
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Conversely, if we limit our play to nickel slots on the
Illinois river boats, we will average a measly 89.85% win rate.
If we decide to limit our serious playing to Nevada, and
stay with $1 slots, we will find our best action in Reno. If we are a
quarter player, then Downtown Las Vegas is the best deal in the
U.S.
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Table 7. Casino Win Percentages
5¢
Win%
Location
25¢
Win%
$1
Win%
$5
Win%
Total
Win%
Nevada
November, 1993
Las VegasDowntown
91.3
95.8
95.1
96.7
95.4
Las VegasStrip
88.9
94.1
95.3
96.3
94.7
Laughlin
87.9
94.6
95.9
96.7
94.9
Reno
91.8
94.1
96.2
97.4
95.4
Lake Tahoe
90.3
93.4
95.6
96.8
94.9
Average
90.04
94.40
95.62
96.78
95.06
89.95
90.91
91.63
94.18
91.25
90.5
91.3
91.9
94.4
91.7
86.3
90.69
93.06
94.37
92.30
92.50
90.90
92.60
NA
91.63
89.33
92.87
94.00
95.17
93.06
Atlantic City
January, 1994
Average
Connecticut
January, 1994
Foxwoods
Illinois
December, 1993
Average
Iowa
January, 1994
Average
Colorado
December, 1993
Average
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Examining an individual slot machine in some detail will
further illuminate how slots are programmed to pay off. We will
analyze a 3 reel, two coin multiplier which pays bonuses on two of
its payoffs. The pay schedule for this machine is shown in Table
8.
Table 8. Pay Schedule for Option 3 Reel 2 Coin Multiplier
Symbols
1 Coin
2 Coins
7B 7B 7B
200
1000
5B 5B 5B
50
150
1B 1B 1B
10
20
AB AB AB
5
10
— — —
1
2
7B = Seven Bar
1B = One Bar
5B = Five Bar
— = Blank or "Ghost"
Bonuses paid on 7B 7B 7B and 5B 5B 5B when two coins are
played.
The first step in analyzing this machine is to break out the
number of symbols (stops) per reel. This particular machine has
32 stops per reel and the reel analysis is shown in Table 9.
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Table 9. Reel Analysis Option 3 Reel 2 Coin Multiplier
Number of Symbols per Reel
Symbol
Reel 1
Reel 2
Reel 3
7B
2
1
1
5B
5
4
4
1B
9
9
9
—
16
18
18
With 3 reels of 32 symbols each, we have a total of 32,768
combinations of symbols possible (32 x 32 x 32 = 32,768). Since
bonuses are offered when the second coin is played, we will add
another 32,768 different combinations with play of the second
coin. On this machine, we will use totals of 32,768 combinations
with one coin played and 65,536 combinations when two coins are
played. Table 10 shows an analysis of all winning combinations
on this machine.
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Table 10. Analysis of Winning Payoffs
# on
Combination Reels
Hits
Deduct
Payouts
1 Coin
2 Coins
Payout%
7B 7B 7B
2 1 1
2
-0-
400
2,000
1.4%
5B 5B 5B
5 4 4
80
-0-
4,000
12,000
14.0%
1B 1B 1B
9 9 9
729
-0-
7,290
14,580
25.6%
AB AB AB
16 18 18
3,136
811
11,625
23,250
40.8%
— — —
16 18 18
5,184
-0-
5,184
10,368
18.2%
Totals
9,131
811
28,499
62,198
100.0
Less
Deducts
- 811
Net Hits
8,320
The first column shows each winning combination. In the
second column, labeled "# on Reels" are the number of symbols
on each reel. For example, for the combination 5B 5B 5B, there
are five 5B symbols on the first reel, 4 on the second reel and 4 on
the third reel. Following this same combination of symbols across
the table, the next column shows the total number of winning
combinations (called Hits). For the 5B 5B 5B combination, we
have 5 x 4 x 4 = 80 hits. The next column, labeled Deduct shows
the number of times that a symbol is used in computing a different
payoff, with the same symbol used. It is deducted so that we don't
count the same symbol twice. You will notice that in the row for
AB AB AB we deduct 811 hits from the total number of hits for
this combination of symbols. This is done because 729 of the Bar
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symbols will be the combination 1B 1B 1B and 80 of the Bar
symbols consist of the combination 5B 5B 5B for a total of 811
Any Bar hits which have been included in different payoff
combinations.
The Payout Columns are broken down into payouts for one
and two coins played. The amounts in these columns have been
computed by multiplying the payoff for each combination of
symbols, as shown in Table 8, times the number of Hits for that
combination. Returning to the 5B 5B 5B combination, we
compute the payouts for one coin as 80 Hits x 50 coins for a
payout of 4,000 with one coin played. When two coins are played
and this combination shows, we compute the payout as 80 Hits x
150 coins = 12,000 coins, reflecting the bonus payoff.
If we add up the total number of hits, we have a total of
9,131 hits, before deducting overlapping symbols. Deducting 811
for overlaps gives us a net total of 8,320 hits which will pay off on
this machine.
To compute the amount the slot will retain, we divide the
total number of payouts by the total number of possible
combinations for:
Payouts
# of
Payouts
Payout
Total
Combinations Percent
1 Coin
28,499
32,768
86.97%
2 Coins
62,198
65,536
94.90%
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If you will look at the last column in Table 10, showing the
Payout Percentages you will notice that almost 85% of the payouts
occur on the lower paying combinations which pay out 1, 5 and 10
coins with only one coin played (18.2% + 40.8% + 25.6% =
84.6%). For ordinary play, the higher paying combinations of 5B
5B 5B and 7B 7B 7B, with a combined percentage of the machine
payout of about 15% (1.4% + 14.0%), are much less relevant to
assessing how will this machine will pay for short-term play. File
this fact away for future reference as we shall use this information
as part of our basis for developing our winning slots strategy.
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FINDING THE BEST MACHINE
Everyone who has ever played slots for at least five
minutes seems to feel that they are qualified to find the best slot
machine.
"Best" usually means the "loosest" slot, meaning that the
machine seems to pay out more coins than have been played, at
least for a time period. There are as many theories as there are
people on how to find this elusive machine.
Some people believe strictly in luck. If they were wearing
their lucky hat the last time that they played and won, then they
will ascribe their luck to this hat and be sure to wear it every time
they play.
Others like to talk to the slot machines while they play. I
once played next to an elderly lady who started out telling her
machine to "Be good to Mama, Baby," followed by an occasional
pat on the front of the machine. After about thirty minutes her
tune had changed to "Pay up you tight son of a bitch," followed by
a whack on the machine glass.
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Some folks like to test the temperature of the machine
before they begin playing. If the machine is warmer than the other
machines, then this qualifies the machine as a "hot" one, suitable
for play.
Some people will only insert cold coins into a machine,
claiming that if warmer coins are used, the machine tightens up.
Many players believe that slots should be played only at
night or on the weekends, or some other variation of timing.
Still others believe that the rhythm used in pulling the
handle is the secret. Implementation of this theory includes such
variations as the short hard pull and the slow, almost delicate pull.
Each has its adherents.
Others use the "the attendant must know" theory and ask
the slot attendant which is the best machine to play. A variation of
this is to observe another slot machine when playing and if the
machine has not paid a jackpot in a long time, to consider playing
the machine as it should be ready to pay.
The location within the casino is also important for many
players. Some players claim that aisle machines are the best,
while others believe that the loosest slots are hidden in back
corners so that they don't get much play.
I wish I could tell you that one of these approaches works.
You may consider that I have saved you some money, as each of
these approaches have been touted at one time or another in slot
publications of dubious value. I recently purchased a slot book
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which spent several pages describing how hot and cold machines
are laid out in a casino based on the author's theory of how casino
executives are supposed to think.
I don't have much to say about the "luck" or clairvoyance
theories of slot play. Perhaps some folks got it and some don't. I
know that I don't do very well when I rely purely on luck. If luck
does work, I have the impression that it is a very personal thing,
and I don't have any advice on how you may increase yours vis a
vis winning at slot machines. I am going to assume that you are
like me and believe that luck comes to those who are prepared, so
we will concentrate on becoming more prepared.
The time of day theories are really absurd. Many players
believe that the casinos can push a button inside a slot, or jiggle a
couple of levers and change the payouts. With the microprocessor
controlled slots, the chip itself must be changed to affect the
payout percentages. Changing the chip requires the skill of a
trained technician and several hours work. It is also an expensive
proposition for a casino to be constantly changing its slots. You
can rest assured that slot payouts in a particular casino will not
change with nightfall or from a weekday to a weekend.
Obviously, talking to the machine or even caressing it, is
not likely to have any effect on a computer chip controlled
mechanism. Neither is the temperature of the machine (which is
probably most affected by the temperature around it) nor the
warmth of the coins. Slot machine levers have zero influence on
the random number generating chip controlled machines. The
machines could just as easily be activated by a button (as are the
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video slots) or a pull string. The days of handles activating gears
which determined the rate of spin of the reels are long gone.
All of these theories may occasionally win some money for
their adherents, but consider: Randomly selecting any machine
may work just as well.
We are after something a little more definitive. Let's look
first at some of the characteristics of the different types of slot
machines.
One of the attributes we will look for on any machine is the
ability to play from one to as many as five coins without any
penalty for playing less than the maximum number of coins.
Why? Because we want the flexibility to adjust the size of each
wager dependent upon the exact playing conditions we are facing
at that exact moment.
This condition knocks out of contention any single coin slot
machines. With a single coin slot, the only option we have is to
insert a coin and pull the lever. It is a win or lose proposition, with
no alternatives other than changing machines. To have the best
chance of winning, we will demand the flexibility to vary the
number of coins based on each individual machine's attributes.
With this one condition, we will rule out play on any of the
single coin mechanical machines. This restriction is not too
severe, as these machines can only be found in a few downtown
casinos in Las Vegas, and scattered about other Nevada sites.
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By requiring that no penalty be imposed for playing with
less than the maximum number of coins accepted by a particular
machine, we will also rule out a number of multipliers which do
impose this penalty. We will not want to play on any Option
Multipliers (buy-a-pay) slots as these machines bring additional
symbols into play with additional coins inserted so that with less
than the maximum number of coins played, the number of
winning symbols are severely reduced.
Less obviously, but using the same logic, we will reject
playing on the Multiple Pay Line machines, which accomplish the
same thing as the Option machines by bringing additional pay
lines into play as additional coins are inserted.
A second condition we will impose is that the machine we
select to play is a High Frequency machine. By high frequency,
we mean that the machine has been programmed to pay off many
lower payoffs more frequently rather than a very small number of
higher payoffs.
Table 15 compares the hypothetical payoffs of Low and
High Frequency slot machines.
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Table 15. Comparison of High and Low Frequency Slots
High Frequency Payoffs
Low Frequency Payoffs
Payoffs
(# Coins)
Percent of
Total Paid
Out
Payoffs
(# Coins)
Percent of
Total Paid
Out
2
20%
2
10%
10
49%
5
10%
20
25%
10
25%
100
1%
15
32%
1000
18%
Total Payoffs
95%
95%
If we look at the payoff schedules on these two machines,
we don't have much of a clue as to which is the higher or lower
frequency machine. Both machines have similar payoffs, and both
machines will ultimately pay back 95% of the coins played.
Having the benefit of using this table, we can see that the high
frequency payer will return a higher percentage of the coins played
on the payoffs of 20 coins or less. If we add the payoff
percentages for all payoffs of 20 coins or less on the high and low
payoff machines, we find that 94% of the payoffs on the high
frequency version are for payoffs of 2, 10 or 20 coins, while only
77% of the low frequency machine payoffs are for 2, 5, 10 and 15
coin payoffs.
For our purposes, the machine paying 94% of its payoffs on
payoffs ranging from 2 to 20 coins is the better machine, as it is
more likely that we will hit one or more of these payoffs in short-
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term play. While the lower frequency machine returns exactly the
same overall payback of 95%, it accomplishes this by making
fewer lower coin payouts and concentrating a higher amount of its
payback in the less frequently hit jackpot payoff of 1,000 coins.
In short-term play, we are not likely to ever hit the jackpot
payoff. Since 18% of the slot's overall payback is represented by
this jackpot, in simple terms, by not hitting the jackpot, our return
will be reduced by 18%, a large percentage of the expected
payback.
We discussed locations of slots in a general way in the
previous chapter. We found that the best paying slots are located
in the state of Nevada, and on the average, the lowest paying slots
are in Atlantic City. Of course this is from your and my
perspective. If you owned a casino, you would prefer the lower
payout Atlantic City slots.
Another aspect of finding the best slot machine is picking
the best casino in the best location. Unfortunately, casinos are not
very forthright on their exact hold percentages so that this task is
not always that easy.
We can, however, refine our selection process somewhat
without knowing the exact hold percentage of each casino.
First, we know that we should confine our play to casinos.
Grocery stores, service stations, bars, airports and other non casino
locations often have paybacks of from 50% to 75%. Your money
will disappear very quickly if you decide to regularly play the slots
at Joe's All-Nite Market. Needless to say, you should stick with
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legal slot machines. If you decide to play illegal slots, who knows
what extortion will be enacted on you. And you will have little
recourse if you are cheated.
The airport slots at McCarran International Airport are
notoriously tight, although I have been known to play them on
occasion to enjoy a diversion not usually found in the airports of
the world. An elderly neighbor of my mother had an interesting
experience at the Las Vegas airport. His plane was already
boarding when he hit a $100 jackpot on a quarter machine.
Realizing that he did not have time to change the coins into bills,
he began stuffing the quarters into every pocket he had. When he
finally waddled onto the plane, with quarters bulging in every
pocket, his pants fell down from the weight of the quarters. The
entire plane gave him a round of applause.
There are many theories about where the best machines are
located in casinos. Some players believe that machines located at
the end of aisle hold the key to fame and fortune, while others will
swear by different locations. If you have ever read about slots, it
is likely that you were treated to the author's pet theories about
where the best machines were.
To try to separate truth from fiction, I devised a simple
experimental approach. Playing with a group of friends who
agreed to participate in the experiment, we played a number of
casinos systematically and recorded the results. In order to limit
the number of variables for each trip to a casino, we played only
the same denomination machines, e.g. nickel, quarter, dollar or
five dollar machines. Our only variation in these experiments was
the location of the slots in the casinos. Each trial was at least at
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hour long, each player used the same session bankroll, and each
player played at roughly the same speed. Over the years, I was
able to accumulate a number of these trials. While admittedly
deficient in a number of ways (for example we played on slots
manufactured by different companies, rather than same company
slots, and all of our trips were to Las Vegas so that we didn't
"sample" other slot venues), I feel that the results clearly indicate a
pattern of placement of slots by the casino executives.
We refined the terms "loose and tight" to include three
categories of machines:
Loose machines were those whose estimated
paybacks were from 97—99%.
Middle paying machines paid out at from 93—96%.
Tight slots paid out less than 93% of the coins
played.
Let's apply these criteria to different slot denominations.
The tightest slots are without question the nickel slots. We found
virtually no nickel slots that we would term loose. There are some
middle paying nickel slots, but by far the largest category of the
nickel machines fall into the "tight" group. Published industry
payout percentages confirm this. As of the latest information at
this time, nickel slots paid out an average of 90.04% in Nevada,
86.3% in Illinois, 92.5% on the Iowa river boats, and 89.33% in
the Colorado casinos. No information was available on nickel
machines, if any, in Atlantic City or Foxwoods in Connecticut.
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The nickel slots seem to be a special category in terms of
placement in the casinos. Virtually no pattern was detected in
placement of the "better" nickel machines. Perhaps this is because
there are so few nickel slots which are other than tight. If you are
a nickel player, our advice is to strictly look upon this as
recreation, as the chances of winning are poor.
With the quarter, dollar and five dollar machines, we found
definite patterns on placement of the machines. Before discussing
placement, let's talk about the general payback characteristics of
these machines. As you might suspect, the quarters are tighter
than the dollar machines, which are tighter than the $5 machines.
Referring to published data again, in Atlantic City, the
quarter machines paid back at average of 90.91%, the dollar
machines, 91.63% and the $5 machines 94.18%.
In Nevada, these percentages were: quarter machines,
94.4%, dollar machines 95.62% and $5 machines, 96.78%.
At Foxwoods, the paybacks were: quarter machines
90.5%, dollar machines 91.9%, and $5 machines 94.4%.
On the Illinois river boats, the machines paid out: 90.69%
for the quarter slots, 93.06% of the dollar slots and 94.37% on the
$5 slot machines.
In Colorado, the payouts were: 92.87% for quarter
machines, 94.0 on the dollar machines and 95.17% on the $5 slots.
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Sailing out of Iowa, the river boats offered 90.9% for
quarter play, 92.06% for the dollar slots with no $5 information
available.
We found that the location of the slot machine in the casino
had a positive correlation with how tight or loose the quarter,
dollar and $5 slots were.
The pattern we discovered seemed to be based on how
visible the slot machine is to other slot players. The rationale here
seems to be to place the loosest slot machines so that other slot
players will see winners on the looser slots and be encouraged to
continue playing.
There was no apparent pattern to placing looser slots near
outside entrances or on open aisles to "entice" persons casually
walking by to begin playing slots. Likewise, there was no pattern
of looser slots being located in areas where persons stand while
waiting for a show. The overall pattern of slot placement was to
place the loosest machines in the general slot area in the most
visible locations, with a few looser machines scattered in the slot
rows.
Loose machines were invariably placed next to middle or
even tight machines. In no cases did we ever find two loose slots
side by side.
The table game area has some of the tightest slots in the
casino. We surmised that since table game players are not
traditional slot players, and typically only play a few coins in slot
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machines before or after playing a table game, that the casinos
recognized this tendency and accordingly placed their tightest slots
adjacent to the table games.
A surprising development was the discovery that many
middle and loose slots may be located near the coffee shops in
casinos. At first, this location puzzled us, as this would not seem
to fit the pattern of locating the best paying slots near the slot
playing area. One day, several of us had taken a break from
playing at the Frontier, and we commented on the constant noise
of nearby slots as coins fell into the trays and occasional bells and
other assorted noises were emitted by the machines as well as the
players.
A rationale for placing some of the better paying slots near
the coffee shop then occurred to us. Any slot player, taking a
break in the coffee shop could not help but hear the constant
sounds of slot coins falling into trays. For many players, this
would act like a siren call to return to playing the slot machines as
quickly as possible. So placing some of the better paying slots
near the coffee shop did make sense, if the casino's intention was
to encourage even more slot machine play.
Incidently, any slots near any of the upscale restaurants in
the casinos were invariably tight. Apparently the casinos feel that
slot players are more likely to visit coffee shops, or perhaps (and I
doubt this) the casinos were just being more considerate to the
restaurant patrons in reducing the noise level they were subjected
to while dining.
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Overall, the best paying slot machines will be found in the
slot playing area, so long as the machine is not too close to the
table games. In the slot area, the elevated carrousels are a good
place to find the loosest slots. Another location is in areas where
there are one or more slots in a small group, separated from the
main banks of slots, but clearly visible to two of more slot banks.
Another surprise was to find that many casinos place some
of the better paying slots near the slot change booths. If you
observe these machines, you will see that they don't get much play
when the casinos are uncrowded. A typical player will get tokens
and then find a machine away from the commotion that is adjacent
to the change booths. However during peak playing times, after
10:00 at night and on the weekends, players are forced to play the
machines next to the change area because of crowded conditions.
Since this is a highly visible location, we surmised that the
psychology of placing some of the better paying machines here
would be to encourage some the players who have been loosing to
"give it one more try" and play a little longer.
Encouraging slot players to continue playing seemed to be
a clear theme in placement of the looser slots. If you think about
this, it makes perfect sense from the perspective of the casino.
Don't waste your money on table players or persons standing in a
show line, as these are not persons who have set about the task of
playing slot machines diligently for some time. The table-show
line players are killing a few moments time, with no real
expectation of winning, so why not accommodate them?
Players in the slots area are attempting a real go at making
some money at the slots. They have already made a commitment
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to play for a time, but they may need a little encouragement as the
casino percentages eat away their bankrolls. So the casino
provides this by placing better paying slots in locations that will
draw the most attention to themselves and help give the
discouraged players some incentive to keep playing a little longer.
We summarize the rules for finding and playing the
best slots:
1. The best paying slots, on the average, will be found in Nevada.
Just picking any casino in the state and any slot in the casino will
give you a shot at winning about 95% of your wagers. On the
other hand, if you choose to play in Atlantic City, your average
machine will pay you only about 91%. If you would like a
different experience, try one of the Colorado casinos in the
revitalized mining towns where slots are available. In any
Colorado casino, the average machine will pay about 93% back.
In Blackhawk, the dollar machines pay back an average of 94.5%.
2. Avoid playing in roadside locations, grocery stores, bars,
airports and stateline locations. Never play illegal slots. Do play
in casinos.
3. To use the Ladder Approach, described in the following
chapters, only play Multipliers which offer the ability to play any
number of coins without any penalty for playing less than the
maximum number of coins. Option Multipliers (buy-a-pay) and
Multiple Pay Line machines will be avoided. Of course, the
pattern method of play, described earlier, can be played on any
multiplier, even a progressive.
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4. Play High Frequency Payoff slots. We want to play a machine
that pays off frequently. Jackpot slots, including progressives and
linked-progressives, such as Megabucks, will be avoided.
5. Avoid playing nickel slot machines as these machines are the
tightest in the casinos. Play either quarter, dollar or $5 slots. We
prefer to play the dollar machines, as the bankroll requirement is
not excessive and the paybacks can be generous.
6. Never play two adjacent machines simultaneously. If you have
found a loose machine, the machine next to it won't be.
7. Pick your spot in the casino carefully. Below are our rules for
finding the highest paying (and avoiding the tightest) slots in the
casino:
Machine to Play:
a. Slots outside the coffee shop.
b. Slots near the slots change booth.
c. Slots in visible locations in the slots area, such as
in areas where slot aisles cross and on elevated
carrousels.
d. At any highly visible location from the slot
aisles.
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Machines to Avoid:
a. Aisles of slots around table game areas.
b. Aisles that table game players use to get to the
elevators or go outside.
c. Slots near show and ticket lines.
d. Slots near the sports book.
e. Slots highly visible from the table game area.
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THE LADDER APPROACH
You should now have a good idea about the type of
machine you will want to play and where it may be found.
Assume that you are on the Las Vegas Strip in one of the
posher casinos. You have surveyed the casino and picked out a
Standard Five Coin Multiplier, located at a junction of two slot
aisles in a small group of four machines in plain sight of two slot
banks. You have reviewed the pay schedule on the front of the
machine, and it is not a jackpot machine; in fact, it shows a
number of smaller payoffs. Based on everything you have learned
from this book, you decide to play this slot.
You now face the decision of how to play this machine.
You remember that this book emphasized that you pick out a
machine which accepts multiple coins without penalizing you for
playing less than the maximum number of coins on each pull.
Now what do you do about it?
One of the most effective ways of playing any slot, which
meets all of our other criteria, is The Ladder Approach. With
this approach we will vary the number of coins we put in the
machine per play, starting with a single coin and gradually
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increasing the number of coins played until we reach the
maximum number of coins accepted by the machine. In a sense,
we will climb the "ladder" of coins invested in the machine by
starting at the lowest rung and increasing our wagers as we move
up the ladder.
We will set up this ladder of bets in such a way that a slot
payoff paying ten, or in some cases twenty, times the amount of
our wager, will result in a win for all coins invested prior to that
win for this round of play.
Let's look at the pay schedule for the machine we have
picked to play. Table 16 shows the pay schedule for this Standard
5 Coin Multiplier.
Table 16. Sample Standard 5 Coin Multiplier
Symbols
1
Coin
2
Coins
3
Coins
4
Coins
5
Coins
3C 3C 3C
100
200
300
400
500
2C 2C 2C
20
40
60
80
100
1C 1C 1C
10
20
30
40
50
Any 3 Cherries
2
4
6
8
10
C = Cherry
3C = Three Cherry Cluster
2C = Two Cherry Cluster
1C = One Cherry
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Our basic pay schedule for this machine is 2—10—20—
100 (shaded in table), which when multiplied by the number of
coins played, expands to the full schedule shown above.
For this machine, we decide to devise a ladder such that
any win of 10 times the coins inserted for that play will result in a
net win for that round of play. Our ladder will consist of the
following wagers:
The first nine wagers will be for 1 coin per play.
The next five wagers will be 2 coins per play
The next three wagers will be 3 coins per pull.
The following three wagers will be 4 coin wagers.
The final two bets will be 5 coin wagers.
Table 17 shows the effect that any win paying ten times the
number of coins inserted will have on our investment for a round
of play. You may think of 22 individual plays, or the number of
plays needed to hit a 10x or greater payoff, as a round of play.
Completion of a round of play (when a round requires 22
individual plays) requires inserting a total of 50 coins, as shown in
the table.
The first column in Table 17 tracks the number of pulls or
plays. The second column, "Coins," shows the number of coins
inserted for each play. The third column "Total Coins," shows us
the cumulative amount of our investment in this round.
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Table 17. Ladder Winnings for 5 Coin
Standard Multiplier, 10x Win
Pull
Coins
Total
Coins
Any
10x Win
Minimum
Win (10x)
1
1
1
10
9
2
1
2
10
8
3
1
3
10
7
4
1
4
10
6
5
1
5
10
5
6
1
6
10
4
7
1
7
10
3
8
1
8
10
2
9
1
9
10
1
10
2
11
20
9
11
2
13
20
7
12
2
15
20
5
13
2
17
20
3
14
2
19
20
1
15
3
22
30
8
16
3
25
30
5
17
3
28
30
2
18
4
32
40
8
19
4
36
40
4
20
4
40
40
-
21
5
45
50
5
22
5
50
50
-
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The next column displays the amount, in coins, of any 10x
win. The final column, "Minimum Win," tracks the minimum win
that any 10x payoff will provide. We can see, for example, that if
we hit on play 15, our net win for this round will be at least 8
coins. If we win on play 19, our net round win will be at least 4
coins.
Table 18 summarizes ten rounds played on this machine,
using The Ladder Approach. The left hand column shows the
round of bets, with
Table 18. Ten Rounds on Sample 5 Coin
Multiplier — Ladder Approach
Net
Lost—
Round
Total Amount
Won (Lost)
(32)
(32)
Game
1
22
2
11
3
22
4
15
5
22
(40)
(57)
6
22
(44)
(101)
7
17
61
+38
(63)
8
13
13
+25
(38)
9
2
2
+18
(20)
10
14
14
+27
+7
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Pulls to
10x Win
Net
Won—
Round
Number of
Pulls
33
+7
(25)
(38)
37
+46
(17)
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each round consisting of either the number of pulls needed to hit a
payoff of 10x or greater, or the number of pulls needed to
complete a round of wagers. The second column, "Number of
Pulls," is the number of pulls required to complete a round. In
Game 1, we see that 22 pulls were required to complete the round.
This means that no payoff of 10x or more occurred in 22 plays.
The third column, "Pulls to 10X Win," recaps the total
number of pulls needed to hit a 10x or greater payoff. Starting
with Game 1, we see that a payoff did not occur until pull 11 in
Game 2, with a total of 33 pulls required (22 plays from Game 1
plus 11 plays from Game 2).
The next three columns show the amount won or lost for
each round or game and the Total Amount Won or Lost
throughout this session of play. Reviewing this column, we see
that the most we were ever up was 7 coins in Game 10.
You may have wondered why we carried out the 4 and 5
coin wagers (see Table 17) to the point where a 10x would only
break even. We did this because a number of lesser payoffs will
typically occur in a round of bets, so that even if a 4 coin wager on
pull 20 shows a break even situation in the table, it is likely that
lower payoffs would have occurred by this point in a round of play
so that we will have a net win.
If we analyze Game 7 shown in Table 18 we can illustrate
this point. The payoffs in Game 7 were for 2, 4 and finally 60
coins, for total payouts of 66 coins. By the time we hit a 20x
payoff on play 17, our investment was 28 coins, leaving a net win
of 38 coins for the round. Even though we don't consider a round
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of play completed when we receive lower payoffs, in this case 2
and then 4 coins, these payoffs certainly contribute to our overall
winnings.
A net win of 7 coins with 160 pulls may not seem like
much of a win. However, if we consider that 300 pulls per hour
would not be considered fast play for a slot machine, then this win
would be equivalent to about 13 coins an hour. On a dollar
machine, if the machine continued to pay at about the same rate,
we would win $13 an hour.
Wow, you say, "A whole 13 bucks an hour!" We admit
that this is not much of a win rate for this machine. However, we
did not hit the jackpot while playing this machine. We used our
selection criteria to pick out a likely machine, which does not
guarantee that every slot you play will be a winner. While we
may sniff a little with disdain at a measly $13 an hour win,
consider this: We invested half an hour in this machine, and while
we didn't win much, we didn't lose. We have our original
bankroll, plus a little more, so that we have not been hurt in our
quest to find a better paying machine.
If we had played this same machine making flat bets, our
results would have been considerably different. By "flat bet," we
mean making the same wager over and over, regardless of what
our payoffs are. When we played this machine, we recorded the
results of every pull. This is not something you ever need to do,
but we did it so that we could analyze the results of our play in
some detail.
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With the results of every play recorded, we could, in effect,
go back over the same results and play them in a different manner,
at least on paper. That's what we did with the session shown in
Table 18. We "paper played" these same pulls making a wager of
1 coin per pull, and never varied the number of coins inserted for
each play. Table 19 shows what this session looked like.
Table 19. Ten Rounds on Sample 5
Coin Multiplier — Flat Bets of $1
Games
Played
Pulls to
Win 10x
Win or
Greater
Total
Coins
Won
Total
Coins
Invested
Net Win
(Loss) per
Session
1—2
33
14
33
(19)
3—4
37
24
37
(13)
5—7
61
34
61
(27)
8
13
22
13
+9
9
2
20
2
+18
10
14
24
14
+10
(22)
Total
If we consider that we invested a total of 160 coins and lost
22 coins, our loss rate was 13.75%. If this loss rate were to hold,
it would indicate a payback rate of about 86% for this slot
machine. We can not make sweeping conclusions about a
machine based on only 160 pulls. It may be set to pay only 83%
or as high as 93%. We can probably conclude that it is a tight
machine, and one that we don't want to continue playing.
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Please note that no matter what our flat bets were, we
would still have a loss playing this machine. If we played 2 coins
per pull instead of 1 coin, our loss for this session would have
been 44 coins. At 3 coins per pull, our loss would have been 66
coins. Even if we had hit the 100 coin payoff on this machine, our
results using The Ladder Approach would still be superior to flat
betting.
So much for the books that advise you to always insert the
maximum number of coins. While the amount you win with a
high payoff hit may be less using The Ladder Approach than if
you were inserting the maximum number of coins per play, your
overall winnings will nearly always be greater than with any flat
wagering approach. And as we saw in this example, we were able
to make a small profit on a tight machine, which preserved our
bankroll so that we can look for greener pastures.
Let's try to find a better machine. We decide to move over
just one machine, recalling that two adjacent machines are hardly
ever looser machines and since the machine we just played was
tight, we might have better luck at the next one. We look around.
Our playing area is clearly visible from two banks of slots, and in
addition is in a pathway used by many players going from this
slots area to the change booth. It clearly fits our criteria as a
location that a casino would pick to place some of the highest
paying slots. So we decide, having survived a poorer paying slot
in the right spot, that the next machine over might yield better
results.
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The new machine has three reels and is a Standard 3 Coin
Multiplier. The basic pay schedule is a little more complicated
than our previous machine, and pays off as follows for 1 coin
inserted: 2—5—5—10—10—15—15—50.
This machine will have a different ladder as it only accepts
a maximum of three coins. We decide to again target a win of 10x
or greater and to use the follows wagers for our ladder:
The first nine wagers will be for 1 coin per play.
The next five wagers will be 2 coins per play.
The final three wagers will be 3 coins per play.
Table 20 shows how this ladder works considering any win
of 10x or greater our target win. In this case, we may play 17
individual plays to complete a round if no 10x payoffs occur.
Completion of a round of play will require inserting 28 coins, as
shown in the table.
The first column in Table 20 shows the number of plays.
The next column, "Coins," indicates the number of coins to be
inserted for each play. "Total Coins" indicates the total number of
coins played in the round up to, and including that particular play.
For example, when we have completed Pull 13, we will have
played 17 coins. The "Any 10x Win" column recaps the minimum
amount of an individual win we will consider to call a round
completed. The last column shows the minimum win we will
have accumulated in a round when a 10x or greater payoff occurs.
As you will recall, we call this our minimum win, as any lower
payoffs which will hit in a round will increase our total winnings
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for that round to an amount greater than the amounts shown in the
table.
Table 20. Ladder Winnings for 3
Coin Standard Multiplier, 10x Win
Pull
Coins
Total
Coins
Any
10x Win
Minimum
Win (10x)
1
1
1
10
9
2
1
2
10
8
3
1
3
10
7
4
1
4
10
6
5
1
5
10
5
6
1
6
10
4
7
1
7
10
3
8
1
8
10
2
9
1
9
10
1
10
2
11
20
9
11
2
13
20
7
12
2
15
20
5
13
2
17
20
3
14
2
19
20
1
15
3
22
30
8
16
3
25
30
5
17
3
28
30
2
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Now that we have our approach figured out, let's play this
machine. Table 21 shows the results of ten rounds of play on this
machine. A round of play consists of the number of pulls needed
to hit a 10x or greater payoff, or to complete all seventeen wagers
in the ladder of bets. We have called each round of play a "Game"
in this table. The column, "Number of Pulls," shows the total
number of pulls required to complete a Game, either by hitting a
10x or greater payoff, or through completing all the wagers in the
ladder.
We hit wins of 10x or greater five times in this session.
Our first win occurred in Game 1 after only 9 pulls. The next 10x
win happened in Game 4, with 45 pulls made between the first and
second win. Twelve pulls later we hit again. This win was
followed by another dry stretch, with 41 pulls required to hit the
next big one in Game 8. Finally, another 28 pulls were needed to
hit our final 10x or greater win and wrap up the session.
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Table 21. Ten Rounds on Sample
3 Coin Multiplier—Ladder Approach
Game
Number
of Pulls
Pulls to
10x Win
Net
Won—
Round
1
9
9
+13
2
17
(4)
+9
3
17
(9)
-0-
4
11
45
+17
+17
5
12
12
+31
+48
6
17
(10)
+38
7
17
(5)
+33
8
7
9
17
10
11
41
28
Net
Lost—
Round
Total Amount
Won (Lost)
+13
+7
+40
+4
+44
+25
+69
This session turned out much better than the session on the
first machine. We won 69 coins in 135 pulls. Assuming that our
playing rate is about 300 pulls per hour, then this win is equivalent
to a win rate of 153 coins per hour. Since this was a dollar
machine, our winning rate was $153 an hour. Now we are starting
to see some progress!
We know that this machine is producing much better than
the first one, but just how much better? We decided to run
through the exact same payoffs, using flat wagers so that we can
compare The Ladder Approach with flat betting.
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Table 22 recounts our experience replaying the same pulls
(through the magic of paper and pencil). This table reflects the
results of playing a dollar a pull, for the same 135 pulls with the
same payoffs.
Table 22. Ten Rounds on Sample
3 Coin Multiplier—Flat Bets of $1
Games
Pulls to
Win 10x
Win
Total
Coins
Won
Total
Coins
Invested
Net Win
(Loss) per
Session
1
9
22
9
+13
2—4
45
47
45
+2
5
12
27
12
+15
6—8
41
41
41
-0-
9—10
28
41
28
+13
+43
Total
In this case our return with flat betting was positive. With a
43 coin profit for 135 pulls, our winning rate was over 30%! Now
we know that no slot machines are programmed to pay over 99%.
This is an example of what can happen on a short-term basis with
a better paying slot machine. Unless this session was a fluke (and
subsequent games on the same machine proved that it wasn't —
we won consistently), this is the machine we are looking for. We
probably have a 98—99% payback slot with this machine.
So, our patience has paid off.
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This is an excellent method for short-term slot play. As we
saw, when we played the first machine, it tends to hold its own
even against some of poorer paying Standard Multipliers.
To use this method is very simple. Your first step is to find
a suitable machine to play. If you have followed our guidelines,
you will not find that this it too difficult. Especially in Nevada,
you will find a variety of casinos and variety of slots
"programmed" to pay out frequently on lower paying payouts.
After finding a suitable machine, you will apply a ladder.
We have had some luck with 20x ladders, but in general, the 10x
approach will offer superior results. In using a 10x ladder, the
only decision you have to make depends on the number of coins
accepted by the machine. We generally stick with three and five
coin multipliers, and you should too. For any Standard Five Coin
Multiplier, the ladder you will use is:
Table 23. Ladder for Five Coin Multiplier — 10x Target
Coins Per Play
Number of Plays
Coins Risked
1 Coin
9
9
2 Coins
5
10
3 Coins
3
9
4 Coins
3
12
5 Coins
2
10
Totals
22
50
If the machine you select is a Standard Three Coin
Multiplier, then you will use the ladder shown in Table 24.
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Table 24. Ladder for
Three Coin Multiplier — 10x Target
Coins Per Play
Number of Plays
Coins Risked
1 Coin
9
9
2 Coins
5
10
3 Coins
3
9
Totals
17
28
In the case of the five coin machines, your risk per round
will be limited to 50 coins; with the three coin multipliers, your
risk is only 28 coins per round. We have had good results with
both types of machines, but because of the lower investment per
round, I have a preference for the three coin multipliers.
The Ladder Approach works on three reel as well as five
reel slots. Seeking more simplicity in my life, I prefer the three
reel machines, although our results have not varied significantly
playing the five reel machines. With microprocessor controlled
machines, it is possible for the three reel machine to have more
possible combinations that a five reeler, and even though I know
this, I still prefer the three reel slots.
After selecting the machine you want to play and picking
out the appropriate ladder, you start playing. After any win of 10x
or greater, the round is over. It is not necessary to memorize
anything to use this method. All you have to remember is the
correct ladder, and this information can be written on a piece of
paper you carry with you.
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I recommend that you separate the number of coins needed
to play a round, 50 coins for the five coin machines, and 28 coins
for the three coin slots. After a round is completed, either by
hitting a 10x payoff or by playing through all of the wagers
without a qualifying hit, you should count the number of coins and
record the results for that round. By doing this, you will be able to
qualify the machine to determine if you wish to continue playing
it.
I generally play ten rounds on a machine, unless the first
few rounds are very poor producers. As you have seen in the
results of play presented in this chapter, it is not uncommon for a
loose machine to have two or even three losing rounds in a row
(look at Table 21 again). The critical factor in evaluating a
machine is the size of the losses. If the losing rounds have
minimal losses, then it is usually "safe" to continue playing a
machine. If the losses start to mount, I usually retreat and find
another machine. With all of the good paying machines available,
you don't want to find yourself chained to a poor producer.
Recording the results of your play does not have to be
elaborate. Just write down the round number, as in "round 1," and
record the number of coins you are up or down for the round, like
"+6." After a few rounds you will began to see a pattern, and after
ten rounds you will definitely know whether you want to continue
playing this machine.
A word of caution. The Ladder Approach is an effective
method of play and will protect your bankroll against a major hit
only on the Standard Multipliers. It is not effective against the
Jackpot machines, against the linked progressives or against the
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Option machines, which do not pay on all symbols unless the
maximum number of coins have been inserted. Use of the system
with these machines may be harmful to your bankroll!
The Ladder Approach is very effective. However, I use it
primarily to evaluate machines. If you decide to make it your
exclusive method of play, you shouldn't do too badly with it.
There is a more powerful method of play, which builds on the
ladder approach. We will next explore this even more powerful
method for beating the slots.
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CYCLE TESTING SLOTS
The Ladder Approach works fairly well because it reduces
the size of the average wager, while it attempts to increase the
amount wagered and therefore the amount won, for winning
wagers.
The relative effectiveness of this simple method of play
brings to mind the question, "Do slots pay off on more or less
regular cycles?"
We know that the microprocessor equipped slots have as
their heart a Random Number Generating program, which ensures
that the programmed payoffs will over the long-term provide a
predictable payout.
We sense, seeing the results that a simple laddering
structure produces, that there may be some predictability to the
microprocessor controlled payoffs.
Let's assume that we are playing a simple coin tossing
game where the possible outcomes are head, tails and "coin on
edge." We will lose when either a heads or tails shows and win
whenever the coin lands on edge. We know that this game is set
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up so that the house will pay out 99% of the coins wagered and
that an "on edge" toss will pay out nine coins for each one played.
We can also reason, that if the 99% payout is correct, the "on
edge" situation will occur, on the average, 11 times in 100 tosses.
We reach this conclusion by analyzing how the outcomes
must occur in order for the house to pay out 99% of the amount
wagered. Table 25 shows the average distribution of coin tosses,
so that the house payback of 99% will be maintained:
Table 25. Distribution of Coin Tosses — 100 Tosses
Outcome of Toss
Number of Tosses
Payouts
in Coins
Losing Wager — Heads or
Tails
89
-0-
Winning Wagers — On Edge
11
99
Total Tosses
100
99
Average Number of On Edge
Tosses
100 Coin Tosses/11
On Edge Tosses =
9.09 Frequency of On
Edge Tosses
We can see from the simple analysis in Table 25 that we
would expect an On Edge Toss to occur every 9.09 tosses or about
11% of the time. Now we have the basis for a betting system.
Since the rules of this game allow us to wager from one to three
coins on each coin toss, we decide to wager only one coin for
eight wagers, and then every ninth wager increase our bet to three
coins. We reason that by wagering in this manner, we will be
betting only the minimum amount (the rules require that you must
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wager every bet in order for the game to continue) when the game
is programmed to take our money, and we will be wagering the
maximum amount when the payoff is expected to occur.
Alas, this betting approach turns out to be a disaster. We
try this system for a total of 88 coin tosses and manage to win only
one of our three coin wagers! Here's the distribution of winning
wagers in 88 coin tosses:
Number of tosses to winning wager
9
7
12
6
10
21
11
12
We decide to analyze the outcome of these 88 coin tosses
more carefully. We total the number of tosses required to make
each winning wager and divide this number by the number of
winning wagers (88/8) to compute that, on the average, a winning
wager occurred every 11 tosses. Please note that for this session
of coin tossing a winner showed up less frequently than we would
expect (the expected frequency of a winner is once every 9.09
tosses or rounded, every 9 tosses). Even if we had made our large
wager every eighth, ninth and tenth coin toss, we would have won
only two times in 88 tosses!
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Our problem in using the average number of tosses to time
our largest wager is that while a winner shows on the average of
every nine coin tosses, this is only an average. As we saw in our
test of 88 coin tosses, while a winner appeared eight times in 88
tosses, only once did the winning wager happen to be on the ninth
toss, even though a win occurred, on the average, once every 11
tosses.
Our idea of putting more money down when a winning
coin toss is more likely to hit may be sound, but our methodology
needs to be improved. Fortunately, the discipline of statistics has
come up with an approach to help us. In analyzing the results of
our coin toss game, we have been concentrating on the arithmetic
average, also known as the mean. This gives us a starting point in
our quest to know when to raise our wagers, but what we really
need to know is "how spread out are our winning hits," rather than
only knowing when they occur on the average.
A statistical measure for determining how much variability
or spread we have in the average number of tosses to achieve a
win, is called the Standard Deviation. The Standard Deviation
measures the variability of the numbers which make up the
average or mean. If we knew just how variable the spread of hits
about the mean was, we could adjust our betting approach so that
we would know when it was about time to increase our wagers
with some reasonable expectation that the probability of a winning
toss was eminent.
The Standard Deviation does just that. Statistics teaches us
that when we have a set of data which approximates a Standard
Normal Distribution (a special term indicating that the data will
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tend to group more heavily about the mean and to appear less
frequently as we deviate more and more from the mean) and if our
data confirms to this standard (and we have every reason to
believe that our sample data does just this), then we can compute
the Standard Deviation for this data and determine just how likely
a given score is to be within a certain percentage of the average of
all of our scores.
Statistical evidence indicates that over two thirds of all
scores of a normal distribution will fall within one standard
deviation of the mean. Think what this means. If we knew the
standard deviation for the coin tossing game, then we could group
our larger wagers within one standard deviation of the mean and
count on winning this larger wager over two thirds of the time.
To compute the standard deviation for a sample of data
looks more difficult than it really is. The formula for computing
the standard deviation for a sample is:
s=
∑ (x − x)
2
n −1
Where,
Σ stands for the summation of data,
x represents each item of data,
x is the average (mean) of the sample of data,
n is the number of items of data, and
s is the statistical representation for the standard deviation for a
sample.
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To solve for s, the standard deviation of our sample of the
number of coin tosses per winner is surprisingly simple. One way
to solve a problem like this is to set up the required calculations in
a table form. Table 26 shows how the problem can be set up.
Table 26. Calculation of Standard Deviation for Coin Tosses
Tosses to
Win
x
Tosses Average
x−x
(Tosses Average)²
(x − x) 2
9
-2
4
7
-4
16
12
+1
1
6
-5
25
10
-1
1
21
+10
100
11
-0-
-0-
12
+1
1
88
-0-
148
We first calculate x , the sample mean, by dividing the total
of Tosses to Win by the number of wins, for 88/8 = 11.0. The left
column in Table 26 shows the raw scores, which represent the
values of x. In the second column, x − x , we calculate the values
of each raw score less the mean. For example, the first value in
the second column was derived by the equation 9 - 11 = -2. In the
third column ( x − x ) 2 , the values in the second column are
squared. The first value in column three is -2² = 4 (a negative
number squared is always a positive number). After the values in
column three are computed, this column is totaled, for a total of
148.
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We now have everything we need to know to solve for the
Standard Deviation except the value of n. This value is simply the
number of items we have in column one, in this case 8 items.
Since our formula calls for using n - 1 as the divisor, this value is
8 - 1 = 7.
Substituting our calculated values, our equation now
becomes
s = √148/7 = 4.598.
There is a much easier way to make these calculations.
Many of the electronic hand held calculators can calculate the
value of s. The calculator I use is the Texas Instruments TI30SLR+ which costs less than twenty dollars. To calculate s is
very simple. The steps are:
Clear Stat Register
Enter Data Set
Calculate Mean
Calculate s
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2nd CSR
9
Σ+
7
Σ+
12
Σ+
6
Σ+
10
Σ+
21
Σ+
11
Σ+
12
Σ+
2ndx
2nd σn-1
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On this particular calculator, the symbol "σn-1" means the
same thing as "s."
While these calculations may seem tedious, they are very
easy to do with the calculator.
We now have computed the values of x and s for our coin
tossing data. We now want to develop a betting series so that we
will be wagering the most money when the coin is most likely to
land on edge, and wager lesser amounts when we are more likely
to lose our wagers.
We first want to reexamine our data. Experience has
shown us that any scores which are too far from the mean will
tend to exaggerate any values calculated with these scores
included in the data. Scores which are more than the value of one
standard deviation above the mean are especially suspect, so we
will want to exclude any values which are greater than the value of
x + s. Substituting the values we have calculated into this
equation, we have x + s = 11.00 + 4.598 = 15.598 = 15.60
(rounded).
Looking at our original data, we see that we have one
value, that of 21, which is greater than 15.60. We now exclude
this value from our data and recompute the mean ( x ) and the
standard deviation (s) with our modified data. The modified data
and the amounts calculated for x and s are:
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Modified Data:
9
7
12
6
10
11
12
Value of x for Modified Data = 9.57
Value of s for Modified Data = 2.37
Using these new values of the mean and standard deviation,
we will now devise a range for betting $1, $2 and $3 which are the
only wagers allowed in the coin toss game.
We will want the $1 wagers on bets where the number of
tosses are less than one standard deviation below the mean.
We will want to bet the largest amount of $3 on tosses
where the number of tosses is greater than one standard deviation
below the mean and less than or equal to one standard deviation
above the mean.
We will wager $2 on bets where the number of tosses is
greater than one standard deviation above the mean, but no more
than two times the average modified mean.
Using the values derived from the modified data, we have:
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Range($1 Wager): R1 = 1 ≤ ( x - s); R1 = 1 ≤ 9.57 - 2.37; R1 = 1 ≤ 7
Range($3 Wager): R2 = R1 + 1 ≤ ( x + s); 8 ≤ (9.57 + 2.37); 8 ≤ 12
Range($2 Wager): R3 = R2 + 1 ≤ (2 x ); 13 ≤ 18.
So our range of wagers is as follows:
Wager $1 on tosses 1 through 7, then
Wager $3 on tosses 8 through 12, then
Wager $2 on tosses 13 through 18.
The purpose of this betting scheme is to make our largest
wagers when the number of tosses is within one standard deviation
of the mean, to wager the least amount when the number of tosses
is less than one standard deviation below the mean and to wager a
medium amount whenever the number of tosses is greater than one
standard deviation above the mean, but less than double the
sample mean.
We use this wagering structure to maximize the probability
that any wins will be on wagers for the largest amount, and most
losing wagers will hopefully be for lower amount wagers.
One way to test this approach is to play three versions of
the coin toss game against the data we have recorded and to
compare the results. We will play a flat bet game, where we never
vary the size of our bets, a Ladder Approach game, and finally, we
will apply what we have learned analyzing the data to play a game
using the results of our cycle analysis.
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If we "replay" the coin toss decisions making only flat
wagers of a $1 a toss, our results are not very good. We recall that
a winner showed up only once every eleven tosses on the average,
which is less than our expected average of about once every nine
tosses. In other words, we had a series of coin tosses where the
house won slightly more than its fair share. This type of variation
is common to all games of chance and is the basis of many players
proclaiming after a session which deviated more in the house's
favor, that they were "unlucky." If they were fortunate enough to
hit a streak where the wins occurred more frequently than would
be expected, many players would feel like they hit a "lucky"
streak.
Since we know that we did not get as many wins as we
might expect on the average, we are not surprised to learn that
with flat betting of $1 a toss, we managed to lose $16 in this
contest. Table 27 recounts the results of flat wagering against
these coin tosses.
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Table 27. Results of Betting $1 a Wager in Coin Toss Game
Tosses
to Win
Amount
Won
Amount
Invested per
Win
Net Amount
Won for Each
Winning Wager
9
+9
9
-0-
7
+9
7
+2
12
+9
12
-3
6
+9
6
+3
10
+9
10
-1
21
+9
21
-12
11
+9
11
-2
12
+9
12
-3
+72
88
-16
If we had decided to make $2 wagers, we would have lost
$32. With $3 flat wagers, our losses would have been $48. There
is no way that we can overcome the house edge in a negative
expectation game with flat betting. The house edge on this
particular series of tosses can be determined by dividing the
amount lost by the amount invested for 16/88 = 18.18%. We can
see in this example how a game with only a one percent
theoretical advantage can extract a much higher percentage from
our wallets in a given session.
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We decide to try The Ladder Approach. We work out the
calculations for a 9x winning wager and come up with the
following ladder:
Wager $1 for the first eight tosses
Wager $2 for the next four tosses
Wager $3 for the final three tosses
After the fifteen tosses in our ladder, if no win
occurs, we will start over and continue laddering our
bets until we have a win. Anytime we have a win
(any win in this game is worth 9 x the wager), we
will start the ladder over.
Table 28 shows the results of using The Ladder Approach
with the same series of coin tosses.
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Table 28. Results of The Ladder Approach in Coin Toss
Game
Tosses
to Win
Amount
Won
Amount
Invested
per Win
Net Amount Won
for Each Winning
Wager
9
+18
10
+8
7
+9
7
+2
12
+18
16
+2
6
+9
6
+3
10
+18
12
+6
21
+9
31
-22
11
+18
14
+4
12
+18
16
+2
+117
112
+5
With The Ladder Approach, we were able to win $5, with
an investment of $112, for a winning rate of 4.46% (5/112 =
4.46%). This is a tremendous improvement over flat betting, and
remember that these results were achieved playing a session where
the house edge was over 18%! There is no question that laddering
the wagers can protect us from losses and even seem to perform
the impossible at times, as in this instance of producing a win
against terrible odds.
How well would we do if we used our Cycle Approach to
betting this series of coin tosses? The Cycle Approach betting
series is:
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Wager $1 on tosses 1 through 7, then
Wager $3 on tosses 8 through 12, then
Wager $2 on tosses 13 through 18.
Table 29 shows the results of applying the Cycle Approach
to the coin toss game. We won $20 playing the same series of
tosses that resulted in the $1 flat bettor losing $16, and The Ladder
Approach player winning $9. If we compare the amount we
wagered in the Cycle game of $142 with the amount won of $20,
we find that by using a betting cycle we were able to improve of
winning rate to 14.08% (20/142 = 14.08). This is absolutely
remarkable for a game which short changed us to the extent of an
18% house advantage.
Table 29. Results of Cycle Approach in Coin Toss Game
Super Slots
Tosses
to Win
Amount
Won
Amount
Invested
per Win
Net Amount
Won for each
Winning Wager
9
+27
13
+14
7
+9
7
+2
12
+27
22
+5
6
+9
6
+3
10
+27
16
+11
21
+9
37
-28
11
+27
19
+8
12
+27
22
+5
+162
142
+20
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We began this chapter by asking the question, "Do slots
pay off on more or less regular cycles?" We approached this
question by examining a hypothetical coin toss game, which only
paid off about every ninth toss when the coin landed on edge. We
examined some data generated by the coin tossing, with the data
examined representing a poorer set of results for the player, as a
winner appeared, on the average, every eleven tosses rather than
every nine tosses. We compared several approaches to playing the
coin toss game, with an emphasis on changing the amount
wagered in response to the likelihood of a winning toss showing.
As may have occurred to you, the similarity between the
coin toss game, where most tosses resulted in a loss, and a slot
machine, where most pulls offer no payback, is not accidental.
Our coin toss game was purposefully designed to mimic a slot
machine programmed to pay back a high return to the player, with
fairly frequent payoffs of about 10 to one. The results of playing
the coin toss game are directly applicable to playing slot machines.
We used the coin toss illustration because in having only one
payoff, it simplified our testing of alternative approaches to
playing the game. However, the results of our testing are directly
applicable to the playing the appropriate high payback, high
frequency Multiplier slot machine.
The results of our testing should prove most instructive.
Table 30 recounts the results of our comparison of playing
methods.
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Table 30. Comparison of Flat Betting, The Ladder
Approach and Cycle Betting in Coin Toss Game
Total
Return
Net Won
or Lost
Return %
Betting Method
Investment
in Game
Flat Betting - $1
88
72
-16
-18.18%
Flat Betting - $2
176
144
-32
-18.18%
Flat Betting - $3
264
216
-48
-18.18%
Ladder Approach
112
117
+5
+4.46%
Cycle Betting
142
162
+20
+14.08%
A comparison of our results in quite interesting. Looking
first at any of the Flat Betting schemes, whether we wagered $1,
$2 or $3 per toss, we managed to lose 18.18% of the amount
wagered. Even wagering only $1 a toss cost us $16 in this session.
We might conclude that flat betting the minimum wager may
allow us to lose more slowly. But why accept such dismal results?
The Ladder Approach offers us a better approach than flat
betting, with a positive return of 4.46% earned with this method.
The average size of the Ladder wager was $1.27, computed by
dividing the Investment in Game by the number of tosses (112/88
= 1.27). With laddering our wagers, our average wager was only
slightly higher than making $1 flat bets, but our results were much
improved.
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Cycle betting improved our results even more. With the
Cycle Approach, we were able to earn $20 on the same tosses that
produced losses with flat betting and gave us an $5 win with
laddering. We invested a total of $142 in this game with cycling,
for an average wager of $1.61 (142/88 = 1.61). Our return
improved to 14.08% of the amount wagered, on a series of wagers
where the house had an edge of over 18%.
In comparing Cycle Betting with Laddering, we can see
that our average wager of $1.61 was somewhat larger with the
Cycle Approach than the average wager of $1.27 in The Ladder
Approach. This occurred because our cycle betting series entailed
concentrating larger wagers at the times in the cycle of coin tosses
when a win was more likely to hit.
"Do slots pay off on more or less regular cycles?" As we
shall see in the next chapter, some do. And the Cycle Approach
helps us to beat these slot machines.
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WINNING WITH CYCLE BETTING
We now want to apply what we have learned to playing slot
machines. We will compare the approaches of Flat Betting, The
Ladder Approach and Cycle Betting to the Standard 3 Coin
Multiplier which was used as an example in the chapter "The
Ladder Approach."
When we were first testing play on this machine, we
decided to target a 10x payoff as our target win for each game, and
we noted the following number of pulls needed before we hit a
win paying 10x or more:
Number of pulls to winning wager
9
45
12
41
28
With these results we decide to analyze these slot machine
pulls. We first add up the total number of pulls and then compute
the average number of pulls. The total number of pulls was 135, if
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we divide this by the number of target wins, we have: 135/5 = 27
= x . Setting up our table to compute the Standard Deviation, we
derive the amounts shown in Table 31.
Since there were 5 wins, the value of n is 5 and n - 1 = 4.
Column one (x) in the table represents the number of pulls to win
a slot payoff of 10x. The second column x - x has amounts
computed by subtracting the value of x from each of the numbers
of pulls to win, as in 9 - 27 = -18, the first derived amount in the
second column. Values in the third column, ( x − x )², were derived
by squaring each of the values in the second column.
Table 31. Calculation of Standard Deviation for
Standard 3 Coin Multiplier
Pulls
to Win
x
9
45
12
41
28
135
Pulls Average
x−x
-18
+18
-15
+14
+1
-0-
(Pulls Average)²
( x − x )²
324
324
225
196
1
1070
Having computed these values, we substitute the values
into the equation for standard deviation for s = √1070/4 = 16.355.
If we use the calculator (Texas Instruments model TI30SLR+) we have:
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Clear Stat Register
2nd CSR
Enter Data Set
9 Σ+
45 Σ+
12 Σ+
41 Σ+
Calculate Mean
Calculate s
28 Σ+
2ndx
2nd σn-1
Remember that on this particular machine, σn-1 is
equivalent to s. Having performed these calculations, we want to
reexamine our original data and see if any of the values are greater
than the value of x + s. Substituting our calculated values, we
have x + s = 27.0 + 16.355 = 43.355 = 43.40 (rounded).
Reexamining our original data, we compare the values with
43.40 and we see that one value, that of 45 exceeds 43.40. We
will modify our original data by excluding this value and
recompute x and s. The modified data and the values computed
for x and s are :
Modified Data:
9
12
41
28
Value of x for Modified Data = 22.50
Value of s for Modified Data = 14.89
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Using the modified values of the mean and standard
deviation, we can compute our betting ranges for this 3 Coin
Standard Multiplier.
We will wager only $1 when the number of pulls is less
than one standard deviation below the mean number of pulls to hit
a 10x win.
We will wager $3 when the number of pulls is greater than
one s below x and less than one s above x .
We will wager $2 when the number of pulls is greater than
s + x , but less than 2x.
Using our values calculated from the modified data, we
have:
Range($1 Wager): R1 = 1 ≤ ( x - s); R1 = 1 ≤ 8.
Range($3 Wager): R2 = R1 + 1 ≤ ( x + s); R2 = 9 ≤ (22.50
+ 14.89);
R2 = 9 ≤ 37.
Range($2 Wager): R3 = R2 + 1 ≤ (2 x ); R3 = 38 ≤ 45.
We are now in position to "play" against the recorded
decisions on our standard 3 coin multiplier, and to compare the
results of flat betting, The Ladder Approach and Cycle Betting.
Let's first try flat betting making wagers of $1 a pull. Table
32 shows the results of flat betting against this series of slot pulls.
This was an extraordinarily good series of slot pulls. The house
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edge on this particular series of pulls can be computed by dividing
the amount won by the amount invested for 43/135 = 31.85%.
This is a good example of what we might call a "lucky" streak.
We know that with flat betting, any house edge on a given series
of wagers will cause a loss, and in this case, playing with
Table 32. Results of Betting $1 a Wager with
Standard 3 Coin Multiplier
Pulls
to Win
Amount
Won
Amount
Invested
per Win
Net Amount
Won for Each
Winning Wager
9
+22
9
+13
45
+47
45
+2
12
+27
12
+15
41
+41
41
-0-
28
+41
28
+13
+178
+135
+43
almost a 32% advantage over the house, we did well with flat
betting. We know that using The Ladder Approach and the Cycle
Approach we did well on our coin toss series which resulted in a
loss for the flat bettor. How will these approaches hold up in a
series of wagers where we have had the best of it?
We will try The Ladder Approach first. As you may recall,
our ladder for this particular 3 coin multiplier is:
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Wager $1 for first nine pulls
Wager $2 for next five pulls, then
Wager $3 for final three pulls.
After 17 tosses in our ladder, if no win occurs, we
will start over and continue laddering our bets until
we have a win. Anytime we have a win of 10x or
greater, we will start the ladder over.
The payoffs offered by this particular slot are: 2-5-5-10-1015-15-50. We will consider a series of wagers completed
whenever our win is for at least 10 times the amount wagered.
Table 33 shows the results of using The Ladder Approach with our
series of slot pulls. The Ladder Approach produced a win of $69,
with an investment of $197, for a winning rate of 35.02% (69/197
= 35.02). Notice that in this case laddering produced only a
slightly higher rate of return than flat betting. Flat betting may
produce a percentage return almost as high as laddering whenever
a series of wagers shows a positive return for the player, as was
the case here, where we enjoyed a positive return of about 32%.
As we noted with the coin toss game, whenever a series of wagers
results in the house retaining an edge over the player, The Ladder
Approach nearly always shows a much higher return than flat
betting. Even though the percentage return for Flat Betting was
almost as high as laddering in this instance, laddering bets still
produced a much higher dollar return, the measure most players
are interested in.
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Table 33. Results of The Ladder Approach with
Standard 3 Coin Multiplier
Pulls
to Win
Amount
Won
Amount
Invested
per Win
Net Amount Won
for each Winning
Wager
9
+22
9
+13
45
+73
69
+4
12
+46
15
+31
41
+55
63
-8
28
+70
41
+29
135
+266
197
+69
If we take the same sequence of pulls and apply the Cycle
Approach, our results are even more improved. Table 34
summarizes the result of using Cycle Betting against these slot
machine pulls. With bet cycling, the results are quite good. We
won $127, playing the same series of slot pulls that resulted in a
$43 win with flat betting, and a $69 win using The Ladder
Approach. Our investment in this sequence of wagers was $314,
with total winnings of $441. Our winning rate was 40.44%
(127/314 = 40.44), for a greater than fifteen percent improvement
over laddering. While this improvement in percentage won is not
earth shattering, the dollars won of $127 were 84% higher than the
amount won with laddering and 195% greater than the amount
won with flat betting.
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With continued testing and comparison of these three
approaches, we have concluded that the greatest percentage
improvements, comparing The Ladder Approach and Cycle
Betting with Flat Betting, result whenever a sequence of slot pulls
produces a negative expectation for the player, that is, when the
player is experiencing what he might term an unlucky streak.
On those occasions when a sequence of slot pulls is
positive for the player, flat betting may produce a return almost as
high as laddering, but laddering and cycling will nearly always
show larger dollar returns. In the two examples examined in this
and the previous chapters, Cycle Betting beat both flat betting and
laddering both in terms of dollars won and the percentage returned
on the amount wagered.
With all slot machines programmed to offer less than a
positive return to a player, sequences with negative expectations
for the player are more common than positive ones. Faced with
this fact, the flat bettor is doomed to lose while the ladder player,
and to a greater extent, the cycle bettor, will have good
opportunities of winning.
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Table 34. Results of Cycle Approach
to Standard 3 Coin Multiplier
Amount
Won
Amount
Invested
per Win
Net Amount Won
for each Winning
Wager
9
+52
11
+41
45
+107
110
-3
12
+65
20
+45
41
+100
105
-5
28
+117
68
+49
135
+441
314
+127
Pulls
to Win
Notes to Table 34:
Plays 1-8, Bet 1 coin
Plays 9-37, Bet 3 coins
Plays 38-45, Bet 2 coins
Table 35 compares the results of the three methods of play
when applied to a Standard 3 Coin Multiplier. You will notice
that in this particular sequence of slot pulls, playing $3 a pull
would have produced the highest dollar return of $129. However,
an investment of $405 would have been required to earn this, and
even more importantly, we are using the benefit of hindsight to
make this determination. As we have seen, flat betting will lose
whenever a series of slot wagers results in a negative expectation
for the player, while laddering and cycling both provide
opportunities of winning.
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In this comparison, Cycle Betting again emerged as the
clear winner. While laddering offers us a simple way to
significantly out perform the flat bettor, the little additional time
required to determine a slot's cycle is well worth the effort and can
result in large improvements in your winnings.
I hope that the mathematics used to determine a betting
cycle has not been too tough for you. I urge you to invest twenty
bucks in a statistical calculator so that you can start using cycle
betting to improve your slot winnings. I have found that cycle
betting, when coupled with the slot selection process we have
discussed in this book, are tried and true combinations to produce
very good and fairly consistent winnings on the slots. A little
investment in time to learn these procedures will pay you back
many times over.
Table 35. Comparison of Flat Betting, The Ladder Approach
and Cycle Betting Playing Standard 3 Coin Multiplier
Betting Method
Investment
in Game
Total
Return
Net
Amount
Won
Return
%
Flat Betting - $1
135
178
43
31.85%
Flat Betting - $2
270
356
86
31.85%
Flat Betting - $3
405
534
129
31.85%
Ladder Approach
197
266
69
35.02%
Cycle Betting
314
441
127
40.44%
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MONEY MANAGEMENT
The Super System of winning at slots requires that you pick
the best machine in the right locale, test the machine using The
Ladder Approach, analyze the results, set up a Betting Cycle and
start playing using the Cycle Approach. In addition, to become a
Super Winner, it is necessary that you use a planned, methodical
approach to money management.
A typical gambler will play slots, or any other casino game,
with whatever money he happens to have at the moment. He will
not keep any records of his wins or losses, and he will typically
continue playing until all of his money is gone. Many times, after
this sad event, the gambling funds are augmented by advances on
the credit card, or other monies that should not be spent gambling
and the final results are pretty much the same. He goes home after
a couple of days of gambling, tired, broke, discouraged and none
the wiser as to how this happened other than he had "bad luck."
You are going to be different. If you have gotten this far in
this book, then you know that winning is more than blind luck.
You have been introduced to a superior system for playing slot
machines, one that far outperforms any other slot system available.
So now you think you've got it made.
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Learning the Cycle Betting Approach to winning at slots is
only half of the battle you face when you decide to engage in
combat with a casino. The biggest obstacle you face in emerging
from the casinos victorious (and by that we mean with more
money than you came in with) is yourself.
The first obstacle you must overcome is deciding what it is
that you want out of playing slot machines. Most people will say
that they want to win, or if they are less honest, they will state that
they play for fun. You have got to be in a much more focused
frame of mind than your fellow gambler. Not only must you want
to win, you must be determined to take all of the necessary steps to
become and remain a winner. You will not play harder than other
gamblers, you will play smarter.
This process of overcoming your own obstacles to success
will begin by planning and controlling the amount of money you
bring and play with in a casino. Your slot money, or bankroll, will
not be whatever amount you happen to have when you walk in a
casino. You will know in advance of your visit how much money
you will need for playing the slots, and you will adhere to a set of
rules to protect this money. Your slot bankroll will be designated
for only that: Slot Machine Play. You will not use this money
for meals, taxis, lodging, shows, or other non-slots activities.
Your slots bankroll will be kept separate and apart from your other
money, and you will keep a running record of your successes and
failures at slots play, so that you always know exactly where you
stand. If this sounds like a lot of work, it isn't. It is easy, and I
dare say fun. Nonetheless, it does require more discipline than
you are probably used to, but the proof is in the bottom line. If
you practice correct money management, as well as the other
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disciplines we have discussed, you will fall into the exclusive and
highly limited group of astute individuals who actually manage to
beat the slot machines.
Let's start with your Slots Bankroll. Your Bankroll is the
amount of money that you bring to a casino for the express
purpose of gambling. The time to decide on the amount you need
and to assemble it is at home, before stepping into a casino. If you
are short of the amount required, your best alternative is to wait
until you have the correct bankroll. If you don't, then your play
will be adversely affected, as you will be playing "short and
scared" which is another way of saying that fear of losing your
bankroll will tend to overshadow your playing to the extent that
you will probably end up doing the very thing you fear: losing
your bankroll.
The amount of your bankroll depends on the length of time
that you plan on playing and the planned intensity of your play. If
you plan on two days of fifteen hours a day slot play, then you will
need a larger bankroll than a person planning a one day visit with
a couple of hours of slots play. You know your own playing style.
I personally feel that fifteen hours a day is way too much slots
play for me; on the other hand, only playing for one two hour
session would leave me feeling unfulfilled.
In addition to your playing style, the denomination of slots
that you decide to play will determine your bankroll as well as
your "gambling comfort level." Stated simply, some folks are
only comfortable playing on quarter slots, while others prefer the
$5 slots. I personally like dollar slots, as they are within both my
budget and my gambling comfort level. I can play on dollar slots,
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knowing that I may occasionally lose, and the size of the potential
losses does not prevent me from enjoying the experience. If you
are playing above your comfort zone (another way of saying
above your head), then your fear of losing will color the whole
experience and you will probably end up losing because you do
not play properly.
Because of the variety of styles of play and the range of
comfort levels, you must decide on the size of bankroll that you
will need. One more factor comes into play in making this
decision, and that is whether you will be playing on three or five
coin multipliers. Play on the five coin machines requires a higher
bankroll, as you must have more coins available for a round of
play. I prefer the three coin multipliers, not only because the
bankroll is less for these machines, but because I have experienced
superior results on the three coin machines.
If you plan on playing just two or three hours a day, then
your daily bankroll will be large enough to accommodate the loss
of four complete ladders on a slot machine. If you plan on playing
longer than three hours per day, I recommend that you bring
enough per day to survive the loss of six ladders.
The amount needed for a ladder is simply the total of all
wagers in a particular ladder. A ladder for a Standard 3 Coin
Multiplier, with a 10x target win is 28 coins as shown below:
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Ladder for 3 Coin Standard Multiplier, 10x Win
Wagers
Total per Level
9 bets of 1 coin
9 coins
5 bets of 2 coins
10 coins
3 bets of 3 coins
9 coins
Total Coins
28 coins
The light gambler, needing a daily bankroll of four times
the 3 Coin Multiplier Ladder, will need to take a daily bankroll of
112 coins (4 x 28 = 112). The player planning on three or more
hours of play per day will need a larger daily bankroll of 168 coins
(6 x 28 = 168).
If you want to play on the Standard 5 Coin Multipliers then
you will need 50 coins per ladder as follows:
Ladder for 5 Coin Standard Multiplier, 10x Win
Wagers
9 bets of 1 coin
5 bets of 2 coins
3 bets of 3 coins
3 bets of 4 coins
2 bets of 5 coins
Total Coins
Total per Level
9 coins
10 coins
9 coins
12 coins
10 coins
50 coins
For light play, the daily bankroll will be four times 50 or
200 coins. The moderate bankroll will be six times 50 for 300
coins.
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The following table shows the daily bankroll needed for
playing $.05, $0.25, $1.00 and $5.00 machines for both light and
moderate play.
Table 36. Daily Bankroll for 4x and 6x Loss Limits
$0.05
$0.25
$1.00
$5.00
3 Coins
$5.60
$28.00
$112.00
$560.00
5 Coins
10.00
50.00
200.00
1000.00
3 Coins
8.40
42.00
168.00
840.00
5 Coins
15.00
75.00
300.00
1500.00
4x Loss Limit
6x Loss Limit
Using this chart is easy. If you like to play quarter slots, for
more than three hours a day, and you will be playing the 3 Coin
Multipliers, then you will follow the row under 6x Loss Limit for
3 Coins to the Column labeled $0.25 and the amount of your daily
bankroll is shown as $42.00. If you only plan on playing a couple
of hours a day on a 3 coin dollar slot, then you will need the
bankroll shown under 4x Loss Limit and $1.00 of $112.00.
Before using this chart you should be honest about your
playing style. If you plan on investing even a moderate amount of
time playing slots, you should pick the higher bankroll amounts
shown under 6x Loss Limit.
The purpose of these daily bankrolls is to give you multiple
shots at beating the slot machines, with defined loss limits on how
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much you will be willing to lose in a day. The term "loss limit" is
just that, the maximum amount you will lose in a day's play before
you stop playing. It is your safeguard against ever losing more
than you can afford. These limits must always be adhered to if
you wish to overcome occasional losses and live to fight another
day. On a brighter note, we also have guidelines for your daily
target winnings, which we will discuss shortly.
In planning a casino excursion, you will need to know how
much your total bankroll should be to match your playing style,
the length of your trip, and the denomination of slots on which you
will play. Table 37 can be used to help you plan your bankroll.
Table 37. Trip Bankrolls for 4x and 6x Loss Limits
$0.25
$1.00
$5.00
2 Days
3 Days+
2 Days
3 Days+
2 Days
3 Days+
3 Coin
$56
$84
$224
$336
$1,120
$1,680
5 Coin
100
150
400
600
2,000
3,000
3 Coin
84
126
336
504
1,680
2,520
5 Coin
150
225
600
900
3,000
4,500
4x Loss Limit
6x Loss Limit
If you have a bankroll put together, say in the amount of
$1,000, then you can use the table to determine the type of
machine you will play and the number of days you are qualified to
play. With $1,000 bankroll, for instance, you could play both 3
Coin and 5 Coin $1.00 slots, for three days or longer. You could
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also reduce the amount of your slots bankroll and play quarter
slots. Or you might decide to allocate a portion of your bankroll to
slots play and use the rest of your bankroll for table games.
If you know the length of a planned casino stay, and are
determined to play 3 Coin $1.00 slots, then the table tells you that
if you are a moderate player (three or more hours a day of slots
play), you will need a minimum slots bankroll of $504.
I left off any information in the table about the nickel slots.
You are not likely to find any nickel slots which are worth playing
(at least not with any serious expectation of winning) so I did not
bother to include any bankroll information about these machines.
In addition to matching your bankroll to your playing style,
you will need to keep track of your bankroll as you play. This is
not difficult. Say that you decide to begin play on a 3 Coin
Multiplier, using a 10x ladder. Since this ladder requires 28 coins,
you will begin play with 28 coins in a slots bucket. As you play
the machine, you will let any winnings fall into the slot tray below
and continue to play using only coins from your bucket. One of
two events will occur which will cause you to pause and count the
coins in the tray. If you hit a 10x or greater payoff, you will have
completed the ladder and you will count the coins in the tray to
determine your winnings. If you complete a ladder without a 10x
or greater win, you will count the coins in your tray to see how
well you did for the round.
You will also need to keep a running count of the number
of pulls so that you know exactly where you are on the ladder. I
will use a small card, which fits in my pocket, and keep a count of
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each level of the ladder. When I have finished a level, I will place
a small mark next to that level on the card. As the round
continues, I will keep a mental count for each level of the ladder
and place a mark on the card when that level is finished. When a
round is completed, either by having made all the bets in the
ladder or through hitting a 10x or greater win, I will count coins
and the number of wagers made and record them on my card.
Table 38 illustrates how such a card may be set up.
Using a card like this makes it very easy to accumulate the
information needed to not only keep track of your bankroll, but to
develop the information needed to cycle analyze the machine.
Let's see how the card has been used in this example. We
began playing this slot using a 3 Coin Ladder, and our first 10x
payoff occurred in round 1 after 16 pulls. As we were playing the
round, we placed a mark as we completed each level in the ladder.
As is shown in column one in Table 38, we placed our first mark
next to "9 — 1 coin" after we had inserted our first nine coins and
completed the first level of the ladder.
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Table 38. Tracking Card for 3 Coin Multiplier
1
2
3
4
9 — 1 coin
/
/
/
/
5 — 2 coins
/
3
/
1
3 — 3 coins
2
Number
of Ladder
5
6
7
8
9
10
Betting
Level
/
Round:
Bets
16
12
17
10
Won (Lost)
+8
+12
-4
+28
Bets to Hit
16
12
-
27
In this round, we also completed the second level, and
placed a mark next to "5 — 2 coins" as we completed this level.
Two bets into the third level of the ladder we hit a 10x payoff, so
we wrote a "2" next to "3 — 3 coins" to record the number of pulls
needed at this level. At the bottom of column 1 we recorded the
information for this round. We had made a total of 16 pulls (9 at
level one and 5 at level two, plus the 2 needed in level 3) so we
recorded this information in the row called "Bets." We next
counted the coins in the slot machine tray. There were 33 coins in
the tray and 3 coins in the bucket for a total of 36 coins. Since a
ladder for 3 Coin play totals 28 coins, it was easy to compute our
round win of 8 coins. We also recorded the number of hits
required to hit a qualifying payoff, in this case 16, recorded on the
row labeled "Bets to Hit." This may seem superfluous in this
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round, but not all rounds end so neatly with a 10x or greater hit
before the ladder is completed, so that recording this information
is important as it is number of hits we use for analyzing a
machine's cycles.
In the next round of play (round 2 in the table), a total of 12
pulls were required to reach a payoff hit. We recorded this
information in the same manner as round 1, noting that 12 "Bets to
Hit" were required. Round 3 did not go as smoothly and we
completed the ladder without hitting a payoff. In this case, we
were blessed with a number of lessor payoffs so that we did not
fare too badly, losing only 4 coins for the round. Please note that
we left Bets to Hit blank for this round, as we had no 10x or
greater payoffs. Round 4 required 10 bets before we hit a payoff.
Here we recorded the 10 bets required for the round in the row
"Bets" and recorded the total number of bets required to hit a
payoff in Bets to Hit. We needed a total of 27 bets to hit this
payoff, 17 from round 3 and 10 from round 4. As you can see, we
added the bets from two rounds to compute the number of bets
needed to hit a 10x or larger payoff.
With the information in this table, we could begin to cycle
analyze this machine. Things seem to be going well at this point.
We have completed four rounds of play and have accumulated
winnings of 44 coins. We might make a preliminary
determination that this is a machine which we will want to
continue playing and we would want to increase our winnings rate
even more by using the Cycle Approach. Here's where we must
be a little more patient. We simply don't have enough information
at this point to compute a cycle. I generally play long enough to
have had at least six 10x or greater hits before I analyze the
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machine. On the "good" machine, this can take anywhere from
seven or eight to as many as ten rounds of play. You will notice
that the sample card shown as Table 38 has 10 columns (rounds)
set up. This is not by accident, as ten rounds is a good
number of rounds to play to develop the information you need to
cycle analyze a machine.
In addition to information which can be used for cycling,
this card contains all of the information needed to record the
results of your play on this particular machine. By recording your
playing results as you go, you will be able to record exactly how
much you have won (or lost, losses do happen you know) when
you have finished a session on this machine.
After I have completed a session on a slot machine, I will
record the name of the casino, the date and the machine location
and the machine number on the other side of the card. This is part
of my personal record keeping which accomplishes several things.
It gives me a complete permanent record on my play on this
machine, records the information I will need to substantiate slot
wins or losses and helps me locate a particularly good machine (or
avoid a bad one) on my next casino excursion. My information on
the reverse of the card might look like this:
4Qs — Las Vegas
May 5, 1994
Machine: Right bank next to slot cashier, 3 down
Machine Number: IGT-43062
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After finishing play at a slot machine, I will total up my
wins and losses and record this information on my Slots Record.
In addition to the amount won or lost, I will record the date, the
casino, the machine number, the ladder used, the machine location
and any comments I think are important. Table 39 illustrates a
partial trip record, for one day of slots play.
Table 39. Slot Record — One Day of Play
Won
(Lost)
Cum
Won
(Lost)
Date
Casino
Machine
Number
4/5/94
4Qs
1829
$28
4 Corner 2
Bank
2 Slot
+145
+145
4/5/94
4Qs
1829
$28
same
+335
+480
4/5/94
GN
4136
$28
3 Corner 1
Bank
1 Slot
+102
+582
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Ladder
Location
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I use my own shorthand for recording the machine's
location, so that I can locate the machine the next time I visit the
casino. Although it is not included in this record, you might want
to note the amount of time you spent playing. Then as you
become even more proficient at winning, you can compute the
amount of winnings per hour of play!
The Slots Record is the basis for figuring the net amount
won or lost on any casino excursion. I also keep a record of trip
expenses, and when I get home, I will deduct all trip expenses
from my casino winnings so that I know exactly how well I did on
a particular trip. There is great satisfaction in having three or four
days of fun and returning with significantly more money than I
started with.
Another key ingredient to winning is controlling the losses
and aiming for target wins. We saw how we used loss limits in
determining the amount of bankroll we would need to play the
slots. When you are playing, it is important that you stick to the
daily loss limits. If your daily limit is 6x a Ladder, and you lose
this amount of money, then your slot's play for that day is finished.
You will not invest any more money in slots that day.
To control losses on individual machines is somewhat of an
art. Assuming that you have picked your machine carefully, using
our guidelines, you should not get hurt too badly using The Ladder
Approach, even on a turkey machine. However, if I lose two
ladders when I first begin playing a machine, I am inclined to
leave that machine. While a loss of two consecutive ladders is not
uncommon on a decent machine, I am unwilling to take the chance
if I have a two ladder loss when I first begin playing.
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So the daily loss limit is further adjusted to a two ladder
loss per machine. Assuming we manage to pick three losers in a
row, we will have a shot at three machines before we reach the 6x
daily loss limit and call it quits.
I also use targeting wins to help smooth out my wins and
losses. By targeting a win, I mean setting up a predetermined
daily profit goal, and when that goal has been reached, calling it
quits for the day. A reasonable daily goal, using the Super Slots
system is to double your daily bankroll. When this goal is
reached, your slots play is over for that day.
A frustrating aspect of Super Slots is that sometimes the
target win is reached all too quickly. If you have planned on four
or five hours of slots play and you hit your daily win target in an
hour and a half, you may feel like you have been cheated on your
planned playing time. I have an easy solution for you.
The best approach is to learn another casino game, such as
video poker, if you want to stick with the machine brand of
gaming, or a table game, such as craps, roulette, baccarat or
blackjack. After hitting your targeted daily slots win, play the
other game for awhile. If you use the style of play that I advocate,
you will have daily loss limits and target wins for each casino
game you play. On more than one occasion I have hit my targeted
slots win in an hour or so, proceeded to the craps table and hit my
targeted craps win in another hour, taken a break, played blackjack
and exceeded my target for blackjack in another hour or two.
While this approach to gambling may leave you some time on
your hands, the sweet feel of victory more than compensates for
any idle time you have earned in your battle against the casinos.
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If you are determined to continue playing slots after
doubling your daily loss limit, then you should put aside all of
your winnings and one-half of your daily bankroll, so that you will
be playing with only enough money to complete three ladders. If
you lose this money, you will quit, with a three ladder win tucked
safely away. If you double this money, then add three more
ladders to your "safe" money and keep on playing as long as you
like.
Either approach can be satisfactory. I prefer changing
games, because I happen to enjoy craps, blackjack, some roulette
and an occasional hour or two of video poker. I recommend that
you try this approach as it will make your casino visit more
interesting, and hopefully even more profitable if you learn how to
beat these games. Silverthorne Publications has excellent
publications on how to beat each of these games, and I
recommend them to you highly.
If you decide to continue with slots after hitting your daily
target win, you won't get hurt if you use my suggestion and lock
up all of your daily bankroll plus half of your winnings.
You probably will find that the most difficult aspect of
mastering the Super System is adjusting to becoming a regular
winner. You won't have the good stories about how a particular
slot machine wiped you out. Your friends may begin to look
askance at you, as you seem to win too much. Many persons
begin to feel guilty when they win, as it just doesn't seem right that
they should be gambling and winning. If you look at your slot
playing as your own little business, with limited amounts to be
invested and certain records to be maintained, you will begin to
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put the experience of winning into perspective. Once you
experience the tremendous satisfaction of planning and controlling
a gambling trip, and returning home with more money than you
left with, you will probably become as addicted to winning as
most folks seem to be to losing.
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SLOTS AND THE IRS
You may not like playing with a partner, but whenever you
hit a jackpot of $1,200 or more, the United States Internal
Revenue Service is ready to step in and become your partner. On
larger wins you are expected to share the largess and to include the
winnings in your taxable income.
The official position of the IRS is that any gambling
winnings must be reported as income, but since most wins are in
the form of cash, most gamblers operate under the principle of
"who's to know," and skip on giving the government its anointed
pound of flesh. However, on wins of $1,200 or larger, the
government has pressed the casinos into a form of uncompensated
government service, and they are required to report your winnings
to the IRS.
If you hit a larger jackpot on a slot machine, the kind that
requires an attendant for the payout, you will be asked for a form
of identification which shows your social security number. When
this occurs, it does absolutely no good to complain to the casino,
as its personnel are probably just as annoyed as you are with the
government intrusion into your and its private business. After
furnishing the casino with suitable identification, you will be
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given a W-2G form — "Statement from Certain Gambling
Winnings." Copy A will be sent to the IRS by the casino, and
Copy B will be given to you to file with your income tax return.
If you don't have any identification with you, or if you
decide that who you are is your business and not the government's,
then instead of receiving a casino check for the jackpot, you will
receive a casino receipt pending your furnishing the casino with
information required by the IRS.
If you are a United States resident, no taxes are normally
withheld from your winnings. If you reside in Canada, 15% of
your winnings will be withheld. If you reside in any other foreign
country, the IRS will withhold 30% of your winnings on the spot.
A bright spot in the government's insatiable thirst for
revenue, is that when you file your tax return, you are allowed to
deduct gambling losses to the extent of gambling winnings. This
is sort of a "heads I win, tails you lose" proposition. If you have
net gambling losses, so sorry Charlie, you can't deduct them; if
you have net gambling winnings, please pay up. Gambling
winnings are reported as gross income, just like salary and interest
income. Gambling losses may be taken as an itemized deduction.
If you normally itemize deductions (you probably do if you own a
home with a mortgage), then you may deduct the gambling losses
(but only up to the amount of your winnings). If you don't itemize
deductions, then the losses will probably not do you much good in
terms of reducing your taxable income.
In order to deduct gambling losses, you must be able to
substantiate them. Here's where your slot record keeping comes in
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handy. You will have recorded every loss on slot machines you
have played. The IRS will accept this record so long as you
supply other substantiating proof that you really were in the casino
playing slots on the date that you claim. To further document this,
you should write down the names of persons who were with you
when you were gambling, and you might want to jot down the
names of any attendants helping you with change. In addition, if
you win a jackpot, you will be assisted by casino management,
and you should ask for their business cards so that you can record
their names. Other documents you should keep are restaurant
receipts, keno tickets, airline tickets, and the invoice for your hotel
room. These items will serve as evidence proving that you really
were where you claimed to be.
If you belong to a slot club, the casino has an account of
your slot play in their casino. Whenever you have an IRS reported
win, you can request that the casino verify your total play by
furnishing a spread sheet of your play. As an alternative, you can
request that a "Statement of Loss" form be furnished by the casino.
An easy way to meet all the IRS guidelines for
documentation is to keep the daily record of slots play, as well as
invoices, receipts and other information from your trip. File all
this information in an envelope. Then when you hit a jackpot, and
the IRS invites itself to share in the banquet, you will be prepared
to minimize the tax impact on your winnings.
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WINNING WITH THE SUPER SYSTEM
We have introduced two types of approaches for playing
slots: simple pattern betting using Dead Pulls to limit losses on
any machine and the more involved Super System. Some slot
jurisdictions have very few of the machines suitable for the Super
System, and on these machines (candidates are any multiplier,
including progressives) I use the location selection rules to find the
best machine. I will then use either the Cycle or Frequency
pattern of betting. While the pattern method is not complicated, it
is sound and is recommended whenever you can't find a machine
suitable for the Super System.
The steps for winning using the Super System are very
straight forward and are easy to use. We will summarize the steps
here, for your convenience. If you don't completely understand
any of the steps, you should refer to the chapter covering the step
to refresh your memory.
1. You will limit your play to only certain types of Multiplier slot
machines. You will play a 3 or 5 Coin Multiplier which does not
penalize you for playing less than the maximum number of coins.
These machines can be identified by reading the pay schedules on
the front of the machines. In playing only these Standard
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Multipliers, you will refrain from playing any of the machines
which do penalize you for playing less than the maximum number
of coins on each pull. These machines include the Option
Multipliers, also called the Buy-a-Pay machines, which do not
pay off on all of the payoff symbols unless the maximum number
of coins are inserted, and the Multiple Pay Line slots which bring
additional pay lines into play as more coins are inserted. By
limiting your play to Standard Multipliers, you will able to play
from one to five coins (depending on the machine) without any
penalty in the programmed payoffs.
2. Among the Standard Multipliers, you will seek to play only
High Frequency payout machines. By High Frequency, we mean
machines that pay off on the 2, 5 and 10 coin payouts frequently.
It is not always easy to identify these machines, however they
usually feature a larger number of the smaller payoffs. Avoid
playing Progressive slots, Linked-Progressive slots and Jackpot
Only machines. Needless to say, any of the specialty machines,
such as the Berthas or the novelty machines, like the horse racing
machines, will not warrant any play.
3. Play slots at the best locations. In general, Nevada offers the
highest paying slots and Atlantic City offers the lowest paying
ones. In the state of Nevada, downtown Las Vegas and Reno offer
the best odds for winning, although with an average payout of
about 95%, any of the casino slots in Nevada offer a fair chance of
winning. Always confine your play to slots in casinos. Slots in
grocery stores, service stations, bars and other roadside locations
should be avoided.
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4. Avoid playing nickel slots. Our studies confirmed that it is
almost impossible to find a loose nickel slot. The penalty for
being allowed to play with a small bankroll is pretty stiff, and you
won't have much luck winning on these machines. In Nevada,
quarter, dollar and five dollar machines all offer acceptable
paybacks. We prefer the dollar machines, as machines paying
97% or higher can readily be found, making these machines
superior candidates for the Super System.
5. The location of the slot machine in the casino is very important.
Our studies revealed that the more visible a machine is to other
slot players, the more likely the machine is to be loose. We also
found that loose machines are very seldom, if ever, placed next to
each other. The practice of some slot players of playing two
adjacent machines is not a good one, as one of the machines is
likely to be tight. Our rules for finding a good machine and
avoiding tight ones are:
a. Avoid playing machines directly next to table
games. Also avoid machines next to where show
and ticket lines form. Avoid machines on aisles that
table game players use going to and from the
elevators. Avoid slots near the sports book.
b. Do play machines near casino coffee shops, near
the slot change booths and on elevated slots
carousels. In general, the more visible a machine is
to other slot players, the more likely it is to be a
good payer.
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c. Play slots on small slot islands, clearly visible
from two or more slot banks.
6. On any slot machine selected to play, first use The Ladder
Approach to evaluate the machine and to protect your bankroll
while you are in the process of evaluating a machine. We prefer
the 3 Coin Multipliers over the 5 Coin Multipliers because the
number of coins needed to complete a ladder is less. We usually
target a win 10 times the amount of coins inserted. Typical
ladders for 3 Coin and 5 Coin Multipliers, with a targeted 10x win
are:
Ladder for 3 Coin Standard Multiplier, 10x Win
Super Slots
Wagers
Total per Level
9 bets of 1 coin
9 coins
5 bets of 2 coins
10 coins
3 bets of 3 coins
9 coins
Total Coins
28 coins
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Ladder for 5 Coin Standard Multiplier, 10x Win
Wagers
Total per Level
9 bets of 1 coin
9 coins
5 bets of 2 coins
10 coins
3 bets of 3 coins
9 coins
3 bets of 4 coins
12 coins
2 bets of 5 coins
10 coins
Total Coins
50 coins
Use of these ladders is optional. We have also had good results
with 15x and 20x multipliers. However, machines matching the
10x formula are more common. You may want to experiment
with different ladders if you find a machine paying off well on 15x
or 20x payoffs.
7. After finding the slot you want to play and determining the
appropriate ladder, you will begin playing the machine. You will
use Tracking Cards like the ones shown on the next page to track
your winnings. You may wish to photocopy these cards for your
use in a casino. Use of the Tracking Card is explained in detail on
pages 73-74. Before beginning a round on a ladder, you will
place the amount of coins needed to complete a ladder in a slots
bucket provided by the casino. Only play coins from the bucket
in each round. At the end of a round, which is signaled either by
hitting a 10x or greater payoff (or any other targeted win you have
selected) or by completing all of the wagers in the ladder, you will
count the number of coins in the slot tray, add the number of
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coins, if any, remaining in the slot bucket and determine the
amount you won or lost for the round. This information will be
recorded on the Tracking Card as well as the number of pulls
needed to hit a target win.
Tracking Card Used for 3 Coin Multiplier
Number of
Ladder
1
2
3
4
5
6
7
8
9
10
Betting
Level
9—1 coin
5—2 coins
3—3 coins
Round:
Bets
Won(Lost)
Bets to Hit
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Tracking Card Used for 5 Coin Multiplier
Number of
Ladder
1
2
3
4
5
6
7
8
9
10
Betting
Level
9—1 coin
5—2 coins
3—3 coins
3—4 coins
2—5 coins
Round:
Bets
Won(Lost)
Bets to Hit
8. Play on the machine long enough to accumulate 6 or more hits
of 10x or greater. Generally, ten rounds of play will be enough to
accomplish this if the machine offers reasonable prospects for
winning. If you lose the first two ladders on a machine, quit and
find another machine.
9. After six or more qualifying hits have been made, you will
analyze the number of pulls needed for each hit. You will
compute s, the Standard Deviation, and x, the Mean, for the
Sample of hits you have recorded. After determining these
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values, you will exclude any hits which required a greater number
of pulls than (x + s). After excluding any values which are too
large, you will recompute s and x for the modified data. The
easiest way to make these calculation is to use a inexpensive
statistical calculator, which may be found in any store where hand
held calculators are sold.
10. Using the calculations for x and s, you will set up the Betting
Cycle to be used on this machine. The approach for either a 3 or 5
Coin cycle is:
3 Coin
Wager
5 Coin
Wager
1 Coin
1 Coin
When number of pulls are between
1 and x - s
3 Coins
5 Coins
When number of pulls are between
( x - s + 1) and x + s
2 Coins
3 Coins
When number of pulls are between
( x + s + 1) and 2 x
Cycle Formula
11. Continue playing with the selected machine using the Cycle
Betting Approach. As you play, be sure to record the results of
each round of play, using the Tracking Card. Sometimes after I
have played for awhile, using Cycle Betting, I will recompute the
Betting Cycle, using the additional data I have accumulated while
Cycle Betting. This approach can refine the Betting Cycle even
more. As you play, keep your target win as well as your loss limit
in mind. Even good machines run through dry periods, resulting
in losses. Use the predetermined loss limit to control any losses.
The typical slot player may be ahead at some point in his play and
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end up losing his winnings as well as his original bankroll. You
do not want to do this, especially after you have had a good win.
Use the Target Win guidelines to "lock up" your slots profits.
12. Learn another casino game, or other diversions you enjoy so
that you will not resist taking a break when it is time. Times to
take breaks are when you are tired, when you have become
frustrated with playing, when you have lost your daily limit, after
hitting the daily target win, or when other scheduled activities
(such as dinner) are planned. There is no reason to become a "Slot
Addict" when using the Super System. The slots are always there
and the system can be used whenever you wish. The value of
learning another game is that you will reduce the risk of "slots
burnout." Even though you should become a regular winner using
the methods in this book, there is no reason that you should play
slots beyond the point where it is enjoyable. I find that my
personal limit for slots play is about two hours at a time. If I still
feel the tug of casino ambience after taking a break from slots, I
will play craps, blackjack, roulette or video poker. I highly
recommend learning a casino table game, such as craps, for slots
breaks. Craps offers the chance to interact with other people, to
handle the dice, if you are so inclined, and is a great source of
relief from slots fatigue.
_______________________
Writing this book has been a monumental effort.
Developing the Super Slots system required untold hours in
casinos, testing each new theory, eliminating the ones that seemed
"good on paper" but failed to hold up under real casino conditions,
and finally refining the system which has been presented in this
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publication. I owe a wealth of gratitude to my colleagues who
assisted me in testing many, many slot machines so that we could
determine where the best ones were located and refine our betting
methods.
The product of this research and effort has been presented
here. I hope that you will find our slot selection methods and
betting approach are worth their weight in gold. I, as well as
friends, associates and acquaintances who have used the Super
System, have experienced excellent results using this approach. It
is my fervent hope that you become a consistent slots winner and
will drop me a line sharing your successes.
I think that this book has given you all the tools you need to
become a Super Slots Winner! So what are you waiting for? Go
out there and Start Beating the One-Armed Bandits!
And good luck!
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